tag:blogger.com,1999:blog-87590902017-02-03T12:10:00.466+00:00P.P. Cook's Tangent SpaceInfrequent comments on maths and theoretical physics as seen from the point of view of a lecturer on a finite contract.Paul Cookhttps://plus.google.com/110983481653378694769noreply@blogger.comBlogger82125tag:blogger.com,1999:blog-8759090.post-22034105268111698562012-03-09T19:52:00.000+00:002012-03-09T19:52:00.145+00:00Is this a simulation?There is reason to suppose that this, all this, is a simulation. Not the least enticing reason, but perhaps a misleading one, is that quantum mechanics tells us that at a small scale the world is described by probabilities and statistics. Not only is it described by a statistical distribution but unless we probe closely the statistical distribution is not rendered for us to notice. This is efficient and puts us in mind of a simulation or video-game where an algorithm decides what will be displayed on screen: if we zoom up close the texture of the simulation breaks down, but how it breaks down into pixels is determined by the rules of the program.<br /><br />Heisenberg took seriously the notion that only what we can measure exists. Not so long ago I enjoyed <a href="http://manjitkumar.blogspot.com/">Quantum: Einstein, Bohr and the Great Debate about Reality by Manjit Kumar</a> and learnt that Heisenberg had been inspired, long before he knew much about matrices or anti-commuting variables, by the track of a charged particle through a cloud chamber. As the particle passes through the vapour of the cloud chamber it ionises molecules around which other molecule condense. Thus a track of condensed vapour is formed following the path of the charged particle/atom/molecule. But, reasoned Heisenberg, although the path appears to be continuous it is actually only a sequence of points which occur where each ion in the vapour is formed - unless it is measured the particle's postion is not known for certain. Of course faced with this thought Heisenberg opted for the wild solution that when the particle's position is not measured it does not exist. In the <a href="http://www.imdb.com/title/tt0340057/">film version</a> of <a href="http://en.wikipedia.org/wiki/Michael_Frayn">Michael Frayn</a>'s play <a href="http://en.wikipedia.org/wiki/Copenhagen_(play)">Copenhagen</a>, Heisenberg is shown being inspired while walking beneath a series of pools of light and then vanishing in the shadows between. It all leads very temptingly to the idea that, just like in a computer game, wheresoever we do not look is not rendered and that the fine-grain detail could be displayed by according to an algorithm. So is this a simulation?<br /><br />Let me take a different tack and wonder whether it might be possible one day (let t tend towards infinity...) to construct a simulator. We might dream of something into which we may project all the information in our most advanced brain-state and where all its functions can be replicated as if in the real world, or perhaps I should say the world we conceive as real presently. It will be informative to think about this notion of the real world. To do so permit me the assumption that there is some grand unified theory possessing a large symmetry and let the simulator we are considering be a perfect simulation. That is there are no flaws in the simulation that would allow the insider, the brain in the vat, to deduce that he/she/it exists inside the simulator (the cat from <a href="http://www.imdb.com/title/tt0133093/">The Matrix</a> is back in the bag, so to speak, and there are no rounding error problems inside the simulator for a messianic figure to take advantage of...). Note that I am taking this to mean this means that machine must encode all there is to know about M-theory in one form or another. Finally let us introduce a new constraint, let the machine be localised, i.e. it is not infinite in any direction - it can fit in a bounded volume, nutshell or even teapot, a big enough teapot. All the assumptions that have been made can be recast as saying we have a quantum gravity simulator in a box, let us call it M-box.<br /><br />M-box buzzes, fizzes, gurgles and pops, and by assumption recreates all the information content of a universe. It must be one hell of a machine. If we suppose it could exist what are the corollaries for the physical description of the universe it exists within and simulates perfectly? Since we assumed it is finite in extent and yet contains all of M-theory must we throw out of M-theory any non-local effects that occur? After all the machine is localised and can recreate perfectly M-theory. By localised I had better emphasise that I mean that its internal workings do not rely on any non-local physical effects. This point is worth some more words. Our usual picture of a computer simulation involves information encoded in 1's or 0's in bits of information, more ambitious quantum computers would build information upon data units that can be in a superposition of two states - these are called qubits. Qubits could be built on electron spin for example. An electron is a relatively simple solution of quantum field theory. For the M-box we would like to build its circuitry on solutions of M-theory; we would like the M-box to be able to excite membranes extending into the compact higher-dimensional space. Membranes can be spun and vibrated, but membranes can also be U-dualised into fivebranes. To take this to its limit the clever M-box we imagine will encode data by U-dualising membranes. We try hard not to think about how it might do this. But we emphasise that the M-box is imagined to encode the full set of M-theory solutions by U-dual rotations of a single membrane. Mathematically the object which encodes all these solutions is the coset $\frac{E_{11}}{{\cal R}(E_{11})}$ where ${\cal R}(E_{11})$ is a real-form of $E_{11}$. Now we may ask the question is there a single solution to M-theory which itself possesses the full symmetries of M-theory. The closest we know of is the BKL cosmological singularity which is expected to carry the symmetries of $\frac{E_{10}}{{\cal R}(E_{10})}$. But awe-inspiring as a cosmological singularity may be it is still not enough to be part of the circuit board of our conjectured M-box. If we did construct such an $E_{10}$ M-box then once we embedded our brain-state inside the simulation we would be able to deduce that some parts of the full $E_{11}$ symmetry are missing (we would probably need some simulated psychiatric help after our simulated selves came to this conclusion). So if one could identify a solution to M-theory which itself possessed a full $E_{11}$ symmetry then we would be in business and M-boxes could start to be rolled off the manufacturing line. However as things stand if we deduce that there is an $E_{11}$ symmetry to M-theory and we wondered if we were simulated we might imagine that the simulator is not an M-box but rather an M'-box (surely this is a catchier name than M-box 360?) which is running in a universe which is governed by M'-theory - which has a larger symmetry than $E_{11}$. The argument is then repeated so that M-box $\subset$ M'-box $\subset$ M''-box $\subset \ldots $. One would agree that this is not an enticing picture for someone looking for a closed description of the universe and hoping that we do live in a simulation. One of the attractions of a Kac-Moody algebra is that it has infinite generators and one might hope yet that a clever way to embed $E_{11}$ inside itself could be found and associated with an M-theory (bound-state) solution. Alternatively keen simulationists might prefer to spend their time in Skyrim instead.Paul Cookhttps://plus.google.com/110983481653378694769noreply@blogger.com1tag:blogger.com,1999:blog-8759090.post-60770305339717530272011-04-20T21:57:00.000+00:002011-04-20T21:57:32.199+00:00Theoretical physics inspires art!<div class="separator" style="clear: both; text-align: left;">No I'm not thinking of the appearance of Bagger-Lambert as a sandwich in Ian MacEwan's Solar. Yesterday Radiohead thanked those of us who bought their album "In Limbs" in mp3 format by giving away two extra songs for free, one of which is called "Supercollider". Unbeknownst to the theoretical physics community the group have been playing it live for a couple of years as you can see from the video link above. The lyrics are pasted below and are inspired, I presume, by some theoretical physics jargon... but how long do we have to wait for a song about supersymmetry? I know Muse have already sung about supermassive black holes, but that was not short for supersymmetric massive black hole as far as I know and there is a band called Slept On the Couch, but I do not think they have intentionally named themselves after a breed of superparticles :) Maybe some physicists out there could form a tribute band called SuSy and the Banshees. They could do a version of Peggy Sue, Peggy SuSy. Or "Killing (spinor) in the name of" by Rage Against the (LHC) Machine? We wait patiently with hope.</div><div class="separator" style="clear: both; text-align: center;"><object width="320" height="266" class="BLOGGER-youtube-video" classid="clsid:D27CDB6E-AE6D-11cf-96B8-444553540000" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,40,0" data-thumbnail-src="http://2.gvt0.com/vi/KB8TXwxwftY/0.jpg"><param name="movie" value="http://www.youtube.com/v/KB8TXwxwftY&fs=1&source=uds" /><param name="bgcolor" value="#FFFFFF" /><embed width="320" height="266" src="http://www.youtube.com/v/KB8TXwxwftY&fs=1&source=uds" type="application/x-shockwave-flash"></embed></object></div><blockquote><span class="Apple-style-span" style="font-family: verdana, helvetica, sans-serif; font-size: 10px; line-height: 20px;">Super collider<br style="clear: left;" />Dust in a moment<br style="clear: left;" />Particles scatter<br style="clear: left;" />Parting from the soup<br style="clear: left;" /><br style="clear: left;" />Swimming upstream<br style="clear: left;" />Before the heavens crack open<br style="clear: left;" />Thin pixelations<br style="clear: left;" />Coming out from the dust<br style="clear: left;" /><br style="clear: left;" />In a blue light<br style="clear: left;" />In a green light<br style="clear: left;" />In a half light<br style="clear: left;" />In a work light<br style="clear: left;" /><br style="clear: left;" />In a B-spin<br style="clear: left;" />Flip flopping<br style="clear: left;" />In a pulse wave<br style="clear: left;" />Outstepping<br style="clear: left;" /><br style="clear: left;" />To put the shadows back into<br style="clear: left;" />The boxes<br style="clear: left;" /><br style="clear: left;" />I am open<br style="clear: left;" />I am welcome<br style="clear: left;" />For a fraction<br style="clear: left;" />Of a second<br style="clear: left;" /><br style="clear: left;" />I have jettisoned my illusions<br style="clear: left;" />I have dislodged my depressions<br style="clear: left;" /><br style="clear: left;" />I put the shadows back into<br style="clear: left;" />The boxes </span></blockquote>Paul Cookhttps://plus.google.com/110983481653378694769noreply@blogger.com4tag:blogger.com,1999:blog-8759090.post-29093333986354417972011-02-08T13:08:00.002+00:002014-02-07T20:52:12.024+00:00Spinorial Representations and Dynkin DiagramsI've been enjoying <a href="http://arxiv.org/abs/1102.0934">String Solitons and T-duality</a> by Eric Bergshoeff and Fabio Riccioni today, which builds upon their work from last year <a href="http://arxiv.org/abs/1009.4657">D-Brane Wess-Zumino Terms and U-Duality</a>. These are impressive papers and you can expect to hear more about them here in the not too distant future, in the meantime I thought I would try and manually resuscitate this old blog with some small comments on spinorial representations that this reading brought to mind. Picture, if you will, the Dynkin diagram for SO(d,d), oh all right here it is:<br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://3.bp.blogspot.com/_PB7-q-qIjgE/TVB8Ip41zJI/AAAAAAAAADQ/qSJVOHYcXhI/s1600/Dynkin_diagram_Dn.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="http://3.bp.blogspot.com/_PB7-q-qIjgE/TVB8Ip41zJI/AAAAAAAAADQ/qSJVOHYcXhI/s320/Dynkin_diagram_Dn.png" height="143" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">The $D_d$ Dynkin diagram otherwise known as SO(2d) one of whose real forms is SO(d,d).</td></tr></tbody></table><div>Let there be d nodes to this Dynkin diagram and let them be numbered along the long leg from left to right 1 to (d-2), and for the two fish-tail nodes let the bottom one be number (d-1) and the top one node d.<br /><br /></div><div>One can form a spinorial representation of SO(d,d) by attaching an extra node, which we will number (d+1), to node (d-1) on the diagram above and considering all the roots associated to the extended Dynkain diagram such that the root $\alpha_{(d+1)}$ appears only once. This has the effect of constructing the representation of SO(d,d) with lowest weight $-\lambda_{(d-1)}$. Usually we work with highest weight representations, in this construction we work from the bottom up building on the lowest weight. This representation will be the spinorial representation.</div><div><br /></div><div>So far not so much fun... But we may well wonder how big is this representation? To this end let us decompose the extended Dynkin diagram to tensor representations of SL(d,${\mathbb R}$) by deleting two nodes. Recall that in order to build the spinorial representation we added node (d+1), which is not shown and held it fixed - there was always one multiple $\alpha_{(d+1)}$ in any root of this representation - well now we will delete this and we will also delete node (d). Deleting node (d+1) gives the vector representation of SL(d, ${\mathbb R}$) of dimension $d$ while deleting node (d) gives the antisymmetric 2-index SL(d, ${\mathbb R}$) tensor of dimension $\frac{d(d-1)}{2}$. We can usefully denote these two representations by Young tableaux:</div><div><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/_PB7-q-qIjgE/TVEywLhSbgI/AAAAAAAAADg/L9kUjzIGf-s/s1600/latex-image-2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/_PB7-q-qIjgE/TVEywLhSbgI/AAAAAAAAADg/L9kUjzIGf-s/s1600/latex-image-2.png" /></a></div>Generically the indices are denoted $a$ and $b$ but can range from 1 to (d). In fact upon deletion of the nodes these tableaux takes specific values $a=d$ and $b=(d-1)$. The dimensions of the representations mentioned above are clear when we let the values $(a,b)$ take all possible values allowed by the symmetry of the tableaux. </div><div><br /></div><div>Now as we construct the spinorial representation more and more Young tableau will appear. How can we tell which ones will show up? As SO(d,d) has a finite-dimensional Lie algebra and as the Dynkin diagram is simply-laced, all roots have the same length and for a given (d) there are a finite number of them. Let each root have root length squared equal to 2. We can embed the roots into a vector space $V_{(d+1)}$ with basis elements $e_1,e_2,e_3\ldots e_{(d-1)}, e_d, e_{(d+1)}$. To do this we must preserve all the inner products encoded in the Dynkin diagram between the simple positive roots - this amounts to us being able to find an inner product which will achieve this. Let the simple positive roots in $V_{(d+1)}$ be </div><div>$$\alpha_{i}=e_i - e_{i+1} \qquad \qquad (1\leq i \leq (d-1))$$</div><div>$$\alpha_d = e_{(d-1)}+e_d+e_{(d+1)}$$</div><div>$$\alpha_{(d+1)}=e_d-e_{(d+1)}$$</div><div>Under the usual scalar product $\alpha_d^2=3$ while all the other roots have squared length 2, as desired. We therefore modify the inner product to be given by:</div><div><br /></div><div>$$<\beta,\gamma>=\sum_{i=1}^{d+1}b_ic_i-(m_d)_\beta(m_d)_\gamma$$</div><div><br /></div><div>Where $\beta=\sum_{i=1}^{d+1}b_ie_i=\sum_{i=1}{d+1}m_i\alpha_i$ and $\gamma=\sum_{i=1}^{d+1}c_ie_i$ and $(m_d)_\beta$ is the number of times the root $\alpha_d$ appears in the simple root expansion of $\beta$. So now all roots have length squared 2 and the inner products are those corresponding to the simple roots of our extended SO(d,d) diagram. For reference one can work out the fundamental weights of SO(d,d) in this vector space basis and for this inner product it is the vector with components $-\frac{1}{2}(1,1,\ldots 1,1,-1,(2-d))$ i.e. it is:<br />$$\lambda_{d+1}=-\frac{1}{2}(e_1+e_2+\ldots + e_{(d-2)}+e_{(d-1)})+\frac{1}{2}e_{(d)}+\frac{(d-2)}{2}e_{(d+1)}$$<br />This looks rather odd but then we are making a peculiar spinor construction by embedding the SO(2d) root lattice inside that of $E_{(d+1)}$. However you can see in the first $d$ entries the usual highest weight for the spinorial representation, see <a href="http://en.wikipedia.org/wiki/Spin_representation">the more usual discussion (without the embedding in $E_d$) in Wikipedia </a>for example (look at the section spin representations and their weights). The more familiar story and the connection to Clifford algebras follows from here. But we continue down our path less travelled...<br /><br /></div><div>We were building up the spinorial representation for which we held $m_d=1$ for all the roots in the representation. We may classify the roots that appear by the number of copies $\alpha_d$ they possess, and that number itself we call the level. So at level $m_d=0$ we find just</div><div><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/_PB7-q-qIjgE/TVGK01SlH7I/AAAAAAAAAEw/c5a0jk_Kkwo/s1600/latex-image-2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/_PB7-q-qIjgE/TVGK01SlH7I/AAAAAAAAAEw/c5a0jk_Kkwo/s1600/latex-image-2.png" /></a> </div></div><div>having dimension d. At level 1 we consider the tensor product and decompose it using the <a href="http://en.wikipedia.org/wiki/Littlewood%E2%80%93Richardson_rule">Littlewood-Richardson rules</a> to find:</div><div><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/_PB7-q-qIjgE/TVEyW-xXApI/AAAAAAAAADc/Z4r4KUGk35E/s1600/latex-image-1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/_PB7-q-qIjgE/TVEyW-xXApI/AAAAAAAAADc/Z4r4KUGk35E/s1600/latex-image-1.png" /></a></div>There are two possible Young tableau at level one but in fact only the first has root length squared equal to two, the second has length squared equal to four. As the roots in the representation all have length squared two only the first Young tableau can exist in the algebra. In fact as we keep going and construct the possible Young tableaux at level two, three, four... only the completely antisymmetric tableaux consisting of $2m_d+1$ boxes have length squared two - as a quick computation using the inner product shows.</div><div><br /></div><div>Finally we have a closed statement that the spinorial representation of SO(d,d) can be represented by a sum of SL(d,$\mathbb R$) antisymmetric tensors of $2m_d+1$ indices. For a finite d this sum of tensors terminates when either $2m_d+1=d$ for odd d, or when $2m_d+1=d-1$ for even d:<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/_PB7-q-qIjgE/TVJ89JnWGnI/AAAAAAAAAFc/blJP1rvieJo/s1600/latex-image-1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/_PB7-q-qIjgE/TVJ89JnWGnI/AAAAAAAAAFc/blJP1rvieJo/s1600/latex-image-1.png" /></a></div>For the even d case the dimensions of the $m_d+1=\frac{d}{2}$ Young tableaux may be summed to</div><div>$$d+\frac{d(d-1)(d-2)}{3!}+\frac{d(d-1)(d-2)(d-3)(d-4)}{5!}+...+d=\sum_{i=0}^{\frac{d}{2}-1}{ d\choose (2i+1)}=2^{(d-1)}$$</div><div>While for odd d there are $\frac{d+1}{2}$ tableaux giving:</div><div>$$d+{d\choose 3} + \ldots + {d\choose (d-2)}+{d\choose d}=2^{(d-1)}$$<br />N.B. for the sums one can use the neat trick of adding or subtracting $0=(1-1)^d$ to $2^d=(1+1)^d$ to prove the two sums above are the same. (Thanks to V. for pointing this out.)<br /><br />Et voila! In both even and odd d we count $2^{(d-1)}$, if we happened to not be interested in SO(d,d) but rather SO(D), where D=2d is even we find the dimension of the spinorial representation is $2^{\frac{D}{2}-1}$. This is one of the two inequivalent Weyl spinor representations (there is one associated to each node in the fish tail of the Dynkin diagram) and together they give a Dirac spinor of dimension $2^{\frac{D}{2}}$. For odd D one has to start with the $B_n$ Dynkin diagram and that's another story...</div>Paul Cookhttps://plus.google.com/110983481653378694769noreply@blogger.com5tag:blogger.com,1999:blog-8759090.post-57124018582207295542008-07-06T13:01:00.006+00:002011-01-26T18:41:03.430+00:00Day Four of Eurostrings 2008<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://bp2.blogger.com/_PB7-q-qIjgE/SHDF3Q2b6qI/AAAAAAAAABM/2Xt98ukeHEc/s1600-h/westmal_d.jpg"><img style="margin: 0pt 0pt 10px 10px; float: right; cursor: pointer;" src="http://bp2.blogger.com/_PB7-q-qIjgE/SHDF3Q2b6qI/AAAAAAAAABM/2Xt98ukeHEc/s200/westmal_d.jpg" alt="" id="BLOGGER_PHOTO_ID_5219889521329171106" border="0" /></a>The morning began breakfastless, and a little breathless, rushing from the shower to the conference. By day four conference fatigue was beginning to set in. It had absoulutely nothing to do with the Belgian-beer filled discussions. None whatsoever. However day four proved to give second wind to the meeting, filled with very interesting talks that I hope to give a flavour of here.<br /><br />The morning review lecture was given by <a href="http://www.physics.ohio-state.edu/directory_pages/detail.php3?id=235">Samir D. Mathur</a>, he does not like horizons, well at least those around black holes. One has to sympathise - is it really acceptable to cut a singularity out of a theory? Mathur prefers a fuzzball picture, where the black hole horizon becomes a statistical entity, emerging macrosopically - the canonical comparison is with temperature in the thermodynamical picture. In thermodynamics the temperature is a statistical quantity that can be measured over a large number of microscopic states, but if you sat on a hydrogen molecule (well<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://bp1.blogger.com/_PB7-q-qIjgE/SHDYWRneVLI/AAAAAAAAABU/UepZE9OBoKs/s1600-h/fuzzball.gif"><img style="margin: 0pt 10px 10px 0pt; float: left; cursor: pointer;" src="http://bp1.blogger.com/_PB7-q-qIjgE/SHDYWRneVLI/AAAAAAAAABU/UepZE9OBoKs/s200/fuzzball.gif" alt="" id="BLOGGER_PHOTO_ID_5219909845320094898" border="0" /></a> maybe you already are, but what I mean is, if you had the molecule's view of a gas) you would be able to say a few things about your nearest neighbours relative velocities, and only with a large amount of time would you collect enough information to speak with confidence of the average molecular speed, or temperature. To a microscopic state the temperature is an odd concept, supposedly the black hole horizon is also an odd concept to a gravitational microstate. The fuzzball proposal functionally aims to reproduce the macrosopic black hole phenomena from collections of microstates. The brane microstates themselves do not have horizons in this setup, the horizon appears in the averaging over a large number of brane states. Old and familiar properties of black holes are reproduced in this picture, light can be trapped behind the horizon by an elaborate setup up of light deflecting states, Hawking temperatures can be reproduced and lately Hawking radiation can be produced by pair-production. For an introduction to the proposal you can read his papers <a href="http://arxiv.org/abs/hep-th/0510180">here</a> and <a href="http://arxiv.org/abs/hep-th/0502050">here</a>. The proposal offers a way to side-step <a href="http://en.wikipedia.org/wiki/Black_hole_information_paradox">Hawking's information paradox</a>. Mathur's discussion of the information paradox can be read in <a href="http://arxiv.org/abs/0803.2030">this preprint</a>, where he aims to make a review using pictures.<br /><br />\begin{digression}<br />Kurt Vonnegut used to use a technique of repeating a small, catchy phrase when something of particular note happened in a sentence of his (e.g. in Cat's Cradle each reference to slipping off the mortal coil earns a: so it goes, or in Timequake ting-a-ling is the catchphrase). I think everytime someone tries to explain something with pictures I would like to insert a cowbell noise. So here's to Mathur: *<a href="http://www.esnips.com/nsdoc/7cd6243d-115f-424a-bbd6-b021039c2672/?action=forceDL">cowbell</a>*.<br />\end{digression}<br /><br />Mathur's title this morning was "Lessons from resolving the information paradox". He threw out the notion two charge non-extremal black holes have a singular throat in the spacetime, the geometry may become complicated but not singular. We heard about<span style="font-size:11;"> <a href="http://arxiv.org/abs/0805.3716">tunnelling in fuzzball geometries</a>, <a href="http://arxiv.org/abs/0711.4817">radiation</a> </span>and<span style="font-size:11;"> <a href="http://arxiv.org/abs/0806.2309">pair-creation</a>, </span>which you can read about in the links.<span style="font-size:11;"><br /></span><br />After coffee, we had talks from <a href="http://personnel.physics.ucla.edu/directory/faculty/index.php?f_name=dhoker">Eric D'Hoker</a> ("Exact 1/2 BPS solutions in type IIB and M-theory"), <a href="http://www.chalmers.se/fp/EN/staff/francia-dario">Dario Francia</a> ("Unconstrained higher spins and current exchanges") and <a href="http://arxiv.org/find/hep-th/1/au:+Chialva_D/0/1/0/all/0/1">Diego Chialva</a> ("Chain inflation revisited").<br /><span style="font-size:11;"><br /></span>Paul Cookhttps://plus.google.com/110983481653378694769noreply@blogger.com7tag:blogger.com,1999:blog-8759090.post-24988193315765422642008-07-03T23:01:00.009+00:002011-01-26T18:40:21.802+00:00Halfday WednesdayWell Wednesday of Eurostrings 2008 was a half day - the afternoon was left free to enjoy the pleasures of Amsterdam, or to work furiously on the latest Bagger-Lambert paper. So, of course, in honour of the half day here's a half-blog entry. Instead of writing only half sentences I will aim to halve my number of full sentences.<br /><br />The weather in Amsterdam understood that it was a half day for our conference. Upto midday it was a balmy 27 degrees <a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://bp3.blogger.com/_PB7-q-qIjgE/SG1vSFTMOmI/AAAAAAAAABE/Wuw0wI_ztkk/s1600-h/DSC00022.JPG"><img style="margin: 0pt 0pt 10px 10px; float: right; cursor: pointer;" src="http://bp3.blogger.com/_PB7-q-qIjgE/SG1vSFTMOmI/AAAAAAAAABE/Wuw0wI_ztkk/s320/DSC00022.JPG" alt="" id="BLOGGER_PHOTO_ID_5218949899643271778" border="0" /></a>and sunny, but as I settled in for lunch an almighty, apocalyptic thunder storm came in, as you can perhaps see in the photo (starring Erik Tonni [left] and Diederik Roest [not left]). Erik and Diederik suggested that Bagger-Lambert theory may be getting too close to the truth for the almighty being's liking, and like the Tower of Babel, was about to be toppled by the ensuing thunderstorm. The storm passed, while I ate a very nice sandwich. I am not suggesting any causal connection between the weather and my digestion, but let's not rule it out.<br /><br />Due to a lack of sleep here in Amsterdam, I all but missed the morning session (not a smart move on a half-day) so I am one of the worst people to tell you what was discussed. However let me put up the titles and one or two suggested papers. Perhaps a fellow Eurostring-ite who may stumble this way can let me know some more about the talks? The schedule was:<br /><ul><li>"Strongly coupled Quark-Gluon Plasma and AdS/CFT" by Edward Shuryak, see, perhaps, the paper<span style="font-size:11;"> <a href="http://arxiv.org/abs/0804.1373">here</a><br /></span></li><li>"Is the AdS S-matrix simple?" by <a href="http://arxiv.org/find/hep-th/1/au:+Janik_R/0/1/0/all/0/1">Romuald Janik</a> (I was told that the short answer is: no)<br /></li><li><a href="http://arxiv.org/find/hep-th/1/au:+Verlinde_H/0/1/0/all/0/1">Herman Verlinde</a> gave a blackboard talk.</li><li><span style=""> </span>"Building a holographic superconductor" by<span style="font-size:11;"> <a href="http://www.physics.ucsb.edu/%7Egary/">Gary Horowitz</a>.</span></li></ul>I caught the final talk, on the relatively hot ;) topic of trying to undertand superconduction through the AdS/CFT correspondence. This was the same topic that Denef discussed on Tuesday, but today the role of the AdS background was emphasised in order to capture the charged scalar field around the black hole. The picture does not carry over to the Minkowksi background. Recall that the AdS/CFT correspondence has been invoked to describe heavy ion collisions and condensed matter physics, and even the quantum Hall effect has had a dual gravitational description given. The aim at present is to find the gravitational dual picture of superconductivity. The aim is to find a black hole solution that at some point grows hair. To read more about this see the preprint<span style="font-size:11;"> <a href="http://arxiv.org/abs/0803.3295">here</a>.<br /></span><br />The afternoon was filled with discussion and imported Coca-Cola.<br /><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://bp1.blogger.com/_PB7-q-qIjgE/SG1rvaKxYOI/AAAAAAAAAA8/_nECJ0krXQE/s1600-h/DSC00024.JPG"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer;" src="http://bp1.blogger.com/_PB7-q-qIjgE/SG1rvaKxYOI/AAAAAAAAAA8/_nECJ0krXQE/s320/DSC00024.JPG" alt="" id="BLOGGER_PHOTO_ID_5218946005414797538" border="0" /></a>The evening with discussion and beer.<br /><br />Your humble correspondent flagellates himself gently for missing the talks.<span style="font-size:11;"><br /></span>Paul Cookhttps://plus.google.com/110983481653378694769noreply@blogger.com0tag:blogger.com,1999:blog-8759090.post-11820522787303385122008-07-01T12:11:00.012+00:002008-07-01T21:49:19.239+00:00Day Two of Eurostrings 2008Another day, another cup of soup and a sandwich for lunch. Today it was ham soup and a pineapple sandwich (my Dutch and my taste buds are not good enough to understand what the other ingredients were).<br /><br />This morning we had a review lecture on the pure spinor formalism by Nathan Berkovits. If you want to learn this formalism, <a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://bp1.blogger.com/_PB7-q-qIjgE/SGqhc45W0mI/AAAAAAAAAA0/P8CsZdcR7CE/s1600-h/DSC00016.JPG"><img style="margin: 0pt 10px 10px 0pt; float: left; cursor: pointer;" src="http://bp1.blogger.com/_PB7-q-qIjgE/SGqhc45W0mI/AAAAAAAAAA0/P8CsZdcR7CE/s320/DSC00016.JPG" alt="" id="BLOGGER_PHOTO_ID_5218160635943506530" border="0" /></a>why not start with the reviews <a href="http://arxiv.org/abs/hep-th/0209059">here</a> (and <a href="http://arxiv.org/abs/hep-th/0511008">here</a> [or the blog article <a href="http://motls.blogspot.com/2005/01/pure-spinor-formalism.html">here</a>]) and then end with the paper <a href="http://arxiv.org/abs/0806.1960">here</a>. If you do this in one-and-a-half hours, but ensure you explain it to yourself very clearly, you will have your own simulation of this morning's nice review. Or, if you are feeling little tired, you could watch the video of <a href="http://indico.cern.ch/contributionDisplay.py?contribId=2&confId=26868">Yaron Oz's l</a><a href="http://indico.cern.ch/contributionDisplay.py?contribId=2&confId=26868">ectures</a> to the CERN winter school.<br /><br />Following Berkovits, Andreas Gustavsson, the third man of the present Bagger-Lambert multiple membranes revolution, spoke on..."Multiple M2's". He included <a href="http://arxiv.org/abs/0709.1260">his paper from last year</a> and <a href="http://arxiv.org/abs/0805.4443">his more recent work</a> on how the membrane triple product identity aids amplitude calculations. His talk was followed by th<span style="font-family:georgia;">irty</span> minutes from <a href="http://www.physics.harvard.edu/people/facpages/denef.html">Frederik Denef</a>, t<span style="font-family:georgia;">alking un</span><span style="font-family:arial;">der </span>the title of "the string landscape of quantum critical superconductors", which refers to work in progress with Sean Hartnoll. The central theme was that there are two landscapes in physics. The string theory landscape, constructed inside a unique fundamental theory (M-theory), with low energy excitations (gravitons, "3-formons" :) and superpartners) and where the intricate landscape is considered "party-spoiling". The second landscape is the condensed matter landscape, constructed from a unique theory (the standard model), with low energy excitations (neutrons, protons and electrons) and where the landscpe is still intricate but is useful. The heuristic message is that these two landscapes may be very similar. Denef gave us a toy model two dimensional array of spin one-half particles that illustrated the idea of quantum critical points - points in phase space where a second order phase transition occurs at zero temperature. The crucial features are all summed up in his graph:<span style=";font-family:georgia;font-size:11;" ><br /></span><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://bp1.blogger.com/_PB7-q-qIjgE/SGqRED2tV_I/AAAAAAAAAAc/M1XZJNyX5_0/s1600-h/quantumcriticality.JPG"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer;" src="http://bp1.blogger.com/_PB7-q-qIjgE/SGqRED2tV_I/AAAAAAAAAAc/M1XZJNyX5_0/s400/quantumcriticality.JPG" alt="" id="BLOGGER_PHOTO_ID_5218142617202415602" border="0" /></a>A second example of criticality involved superconductors and whose features were given by a toy-modelin two dimensions: a Bose-Hubbard model. There is a phase transition between being an insulator and being a superconductor. This picture was to be compared with a charged scalar field in a Reisner-Nordstrom AdS background. The idea (due to Gubser) was that there is a quantum critical point here too that separates insulation from superconductivity. Namely when electrostatic repulsion of the charged scalar is larger than its gravitational attraction towards the singularity in the space-time, then a halo or cloud of charge forms around the black-hole. This is the superconducting picture. Otherwise the charge falls into the horizon and we have the insulating picture. We are to expect to hear more about this superconducting phase from Gary Horowitz tomorrow. Denef told us one could be optimistic that this picture could be constructed in string theory. Citing the<span style=";font-family:georgia;font-size:11;" > <a href="http://arxiv.org/abs/hep-th/0601001">"Gravity=Weakest force" paper of</a></span><span style=";font-family:georgia;font-size:11;" ><a href="http://arxiv.org/abs/hep-th/0601001"> Arkani-Hamed, Motl, Nicolis and Vafa</a></span>, Denef said that Reissner-Nordstrom black-holes should be able to decay and so there was an expectation that the electrostatic repulsion > gravitational attraction regime should exist. Perhaps microscopic physics and macroscopic physics are not so different after all?<br /><br />In the last morning talk, Giulio Bonelli spoke under the title "On gauge/string correspondence and mirror symmetry" and you can read his preprint <span style="font-size:11;"><a href="http://arxiv.org/abs/0804.2629">here</a>. </span>In the afternoon we heard an exuberant Vijay Balasubramanian talk about getting something from nothing. His title was "Statistical predictions from anarchic field theory landscapes". Out of chaos certain coarse-grained properties could become predictable he said, read more in the <span style="font-size:11;"><a href="http://arxiv.org/abs/0805.4196">preprint</a>. </span>The final thirty minute talk of the day was given by Diederik Roest, who talked on my favourite subject: "The Kac-Moody algebras of supergravity". The talk covered decomposition of the algebra, the correspondence between de-forms, top forms and E(11)<span style="font-size:11;"> (<a href="http://arxiv.org/abs/0711.2035">preprint</a>) </span>and also his work with Axel Kleinschmidt on identifying the Kac-Moody algebras that are appropriate to three dimensional scalar theories with a quarter or less of the full supersymmetry<span style="font-size:11;"> (<a href="http://arxiv.org/abs/0805.2573">preprint</a>).</span><span style="font-size:11;"> </span>After coffee, we had a gong show for some researchers but unfortunately we had no gong. Poor Pierre Vanhove must have been kicking himself that he hadn't packed his legendary<span style="font-size:11;"> <a href="http://www.esnips.com/nsdoc/7cd6243d-115f-424a-bbd6-b021039c2672/?action=forceDL">cowbell</a>...</span><br /><br />On my walk back home I encountered two mathematical omens in odd places, first a van that seemed like it could go to infinity and beyond:<br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://bp1.blogger.com/_PB7-q-qIjgE/SGqeOdpMdSI/AAAAAAAAAAs/rxbmfQi3bgU/s1600-h/DSC00015.JPG"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer;" src="http://bp1.blogger.com/_PB7-q-qIjgE/SGqeOdpMdSI/AAAAAAAAAAs/rxbmfQi3bgU/s400/DSC00015.JPG" alt="" id="BLOGGER_PHOTO_ID_5218157089574909218" border="0" /></a>And, second, I saw the hotel I should have been staying at:<br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://bp2.blogger.com/_PB7-q-qIjgE/SGqbL8drT3I/AAAAAAAAAAk/eeFRU8HdfJo/s1600-h/DSC00018.JPG"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer;" src="http://bp2.blogger.com/_PB7-q-qIjgE/SGqbL8drT3I/AAAAAAAAAAk/eeFRU8HdfJo/s400/DSC00018.JPG" alt="" id="BLOGGER_PHOTO_ID_5218153747773607794" border="0" /></a>Unfortunately there were no <a href="http://www.guardian.co.uk/world/2008/jun/30/netherlands?gusrc=rss&feed=networkfront">giraffes helping zebras to escape the circus</a>... despite this bizarre story I'm not sure that truth is stranger than fiction. In fiction the same story could have happened but the giraffe might have been smoking a cuban cigar and saying that he loved it when a plan came together and all the while Pierre Vanhove skipping in front leading the animals with the merry din of his cowbell.<span style="font-size:11;"><br /></span>Paul Cookhttps://plus.google.com/110983481653378694769noreply@blogger.com26tag:blogger.com,1999:blog-8759090.post-2245673559172816012008-06-30T20:41:00.008+00:002008-07-01T19:32:26.651+00:00Eurostrings 2008<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://www.science.uva.nl/research/itf/strings/amsterdam2008/strings2008-header-final_2.jpg"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 400px;" src="http://www.science.uva.nl/research/itf/strings/amsterdam2008/strings2008-header-final_2.jpg" alt="" border="0" /></a>The tram door closed viciously on Pierre Vanhove's rucksack and off it tootled away from Centraal Station (the tram, not the rucksack). My travelling companions were all on board, and only I was left behind with the rest of the amputated tram queue. The man behind me in the queue said "welcome to Amsterdam" in friendly English. We struck up a conversation and he asked what kind of conference I was attending. I told him it was physics, "serious" was his reply. I asked him what he recommended visiting while I was in the city, he said that for him it was all about wandering around and taking it all in. I pushed him and asked for one thing to see in particular, "the red light district". Or perhaps the upstairs floor of a cafe with a particularly good view over a canal that the tourists lack the energy to investigate. Even though my trip to Amsterdam was only beginning I wondered if this mixture of sites might not give a good impression of Amsterdam. From my walks today I am not disappointed. It is a beautiful city, the colourful boats that crowd the canal are laden with multicoloured bric-a-brac, the buildings on the banks appear disordered like the teeth of a friendly giant and yet each and every one appears spic and span upon inspection, even the cyclists speeding unstoppably down neat cycle paths carry their loved ones side-saddle on the back - a jumble of colourful clothes flying behind in the sunlight. For every ordered thing here there is a controlled disorder that is very pleasant to watch.<br /><br />I am here for <a href="http://www.science.uva.nl/research/itf/strings/amsterdam2008/schedule.html">Eurostrings 2008</a>, a smaller, quieter version of Strings, but which is packed with excellent speakers and an interesting crowd of participants. <a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://bp3.blogger.com/_PB7-q-qIjgE/SGl4VcU_OzI/AAAAAAAAAAU/rzKynBbzSpQ/s1600-h/AMS.jpg"><img style="margin: 0pt 0pt 10px 10px; float: right; cursor: pointer;" src="http://bp3.blogger.com/_PB7-q-qIjgE/SGl4VcU_OzI/AAAAAAAAAAU/rzKynBbzSpQ/s320/AMS.jpg" alt="" id="BLOGGER_PHOTO_ID_5217833953062239026" border="0" /></a>You're a String (thanks Per!) is being hosted this year by the University of Amsterdam, apparently it's in the same venue as Strings 1997. The organisation has been superb and we have had an excellent first day of talks which I will try and summarise here (and maybe expand upon later).<br /><br />We began the day hearing <a href="http://en.wikipedia.org/wiki/Ashoke_Sen">Ashoke Sen</a> talking about dyons in N=4 as discussed in his recent papers <a href="http://arxiv.org/abs/0803.3857">here</a> and <a href="http://arxiv.org/abs/0804.0651">here</a>. He described to us the protected index associated to <img src="http://www.forkosh.dreamhost.com/mimetex.cgi?%5Cfrac%7B1%7D%7B4%7D" align="middle" border="0" />BPS states, labelled d(Q,P). Here Q is the electric charge and P the magnetic charge. It is the number of <img src="http://www.forkosh.dreamhost.com/mimetex.cgi?%5Cfrac%7B1%7D%7B4%7D" align="middle" border="0" /> BPS states weighted by <img src="http://www.forkosh.dreamhost.com/mimetex.cgi?%28-1%29%5E%7B2h%7D" align="middle" border="0" />, where <img src="http://www.forkosh.dreamhost.com/mimetex.cgi?h" align="middle" border="0" /> is the helicity. That d(Q,P) is protected means that it does not change under a continuous variation of the coupling constant or moduli of the theory. In fact if the coupling constant is varied onl the BPS states remain and contribute to the counting. However d(Q,P) can make sudden jumps over "walls of marginal stability" - these are places where the <img src="http://www.forkosh.dreamhost.com/mimetex.cgi?%5Cfrac%7B1%7D%7B4%7D" align="middle" border="0" /> BPS states may decay into <img src="http://www.forkosh.dreamhost.com/mimetex.cgi?%5Cfrac%7B1%7D%7B2%7D" align="middle" border="0" /> BPS states. The domain wall itself is defined by four parameters which become discrete due to charge quantisation. Consequently d(Q,P) appears to depend not only on Q and P but also on the domain in which the moduli lie. One can calculate the partition function from d(Q,P) expressed as a function of T-duality invariant terms: <img src="http://www.forkosh.dreamhost.com/mimetex.cgi?Q%5E2,%20P%5E2,%20Q%20%5Ccdot%20P" align="middle" border="0" />, a discrete T-duality invariant and also the domain in which the protected index is calculated. It transpires that the partition function converges after analytic continuation of some of the variables but in "all known examples" the partition function ends up being invariant of the domain one started calculating in. What can one say about how the microscopic dyon partition function reproduces the macroscopic black hole entropy count? Well, first, within the domain of applicabilit of the partition function the entropy calculation is in agreement with the inclusion of the four derivative Gauss-Bonnet terms. So far, so good. But what about the phenomenon of discrete value changes in d(Q,P) as one jumps over domain walls? For the single black hole this microscopic property cannot be reproduced macroscopically, but for the multicentre black holes it agrees perfectly - one can see this is possible since for different values of moduli space multicentred balck holes may cease to exist as one crosses walls of marginal stability. At the end of his talk Sen focussed on how one could work towards a complete comparison between <img src="http://www.forkosh.dreamhost.com/mimetex.cgi?S_%7BBH%7D" align="middle" border="0" /> and <img src="http://www.forkosh.dreamhost.com/mimetex.cgi?S_%7Bmicro%7D" align="middle" border="0" /> (since a number of terms had been exponentially suppressed in the earlier comparison in order to compare like-for-like). The full picture would include both higher derivative corrections and quantum corrections, for the former one can use Wald's formula to make the calculations, for the latter Sen proposes a close scrutiny of <img src="http://www.forkosh.dreamhost.com/mimetex.cgi?AdS_2/CFT_1" align="middle" border="0" /> duality. Starting with the near horizon geometry of a black hole and then analytcally continuing to the Euclidean solution one finds the <img src="http://www.forkosh.dreamhost.com/mimetex.cgi?AdS_2" align="middle" border="0" /> metric. The partition function in this metric is the exponential of minus this Euclidean action, and is used together with a cut off to obtain:<br /><img src="http://www.forkosh.dreamhost.com/mimetex.cgi?Z_%7BAdS_2%7D%5Cequiv%20e%5E%7BKr_0+S_%7BBH%7D-2%5Cpi%20%5Cbar%7Be%7D%5Ccdot%20%5Cbar%7Bq%7D" align="middle" border="0" /><br />By the AdS/CFT correspondence one can exactly calculate the partition function for the CFT:<br /><img src="http://www.forkosh.dreamhost.com/mimetex.cgi?Z_%7BCFT_1%7D%5Cequiv%20e%5E%7B-2%5Cpi%20r_0%20E_0%7D%20%5Csum%20d%28%5Cbar%7Bq%7D%29%20e%5E%7B-2%5Cpi%20%5Cbar%7Be%7D%5Ccdot%20%5Cbar%7Bq%7D%7D" align="middle" border="0" /><br />Where <img src="http://www.forkosh.dreamhost.com/mimetex.cgi?E_0" align="middle" border="0" /> is a rescaled ground state energy. Now the two expressions may be equated and the black hole entropy examined.<br /><br />Ionnis Papadimitriou then spoke to us about how to rigourously define an asymptotically flat spacetime and then considered its holographic description - you can read more about this <a href="http://arxiv.org/abs/hep-th/0505190">here</a>. Pierre Vanhove, minus his infamous <a href="http://www.esnips.com/nsdoc/7cd6243d-115f-424a-bbd6-b021039c2672/?action=forceDL"><span style="text-decoration: underline;">cow bell</span></a>, spoke next on the no-triangle hypothesis (update: why not read <a href="http://motls.blogspot.com/2008/07/two-roads-from-n8-sugra-to-string.html">Lubos' analysis of the situation</a>) for <img src="http://www.forkosh.dreamhost.com/mimetex.cgi?%7B%5Ccal%20N%7D=8" align="middle" border="0" /> SuGra, which is, of course, just <img src="http://www.forkosh.dreamhost.com/mimetex.cgi?%7B%5Ccal%20N%7D=4" align="middle" border="0" /> squared - or at least it has many remarkable similarities to make such a conjecture plausible. It turns out that the no triangle hypothesis should really be called the no-triangles, no bubbles and, in fact, just boxes in the one loop scattering amplitudes hypothesis - but that's not very catchy. For multiloop scattering diagrams, the no-triangle hypothesis informs us about the one-loop sub-terms that remain when one makes suitable cuts in the multiloop diagram. Pierre told us, without once ringing any kind of bell, not for cow, horse, nor wild mountain goat, that since the cancelltations in the gravity theory are due to the (colourless) gauge invariance the hypothesis can also be applied to other theories with less SuSy than <img src="http://www.forkosh.dreamhost.com/mimetex.cgi?%7B%5Ccal%20N%7D=8" align="middle" border="0" />. Pierre finished enigmatically by telling the audience that if <img src="http://www.forkosh.dreamhost.com/mimetex.cgi?%7B%5Ccal%20N%7D=8" align="middle" border="0" /> is divergent he bets that it diverges at 9-loops. He didn't say how much he bets.<br /><br />In the afternoon, following a sparse lunch of soup and a sandwich, <a href="http://www.theory.caltech.edu/%7Eooguri/">Hirosi Ooguri</a> talked under the title of Current Gauge Correlators for General Gauge Mediation - the idea was to extend the region of strong interactions from just the hidden sector to include the mediating sector that gives rise to the visible sector. You can read his paper with his collaborators on this subject <a href="http://arxiv.org/abs/0806.4733">here</a>. After Ooguri, Marco Zagermann told us that <img src="http://www.forkosh.dreamhost.com/mimetex.cgi?%5Cfrac%7BT%5E2%7D%7BZ_2%7D" align="middle" border="0" /> is the pillow, and invited us to revisit D3/D7 brane inflation models. The inflaton is the separation distance between a D7 with flux turned on and a parallel D3. At the end of the period of inflation, cosmic strings condensed - the associated preprint is available <a href="http://arxiv.org/abs/0804.3961">here</a>. Finally Ki-Myeong Lee talked about "New" <img src="http://www.forkosh.dreamhost.com/mimetex.cgi?%7B%5Ccal%20N%7D=5,6" align="middle" border="0" /> Superconformal Chern-Simons Theories. Since this is work related to the increasingly popular multiple M2 work of Bagger-Lambert and Gustavsson, Lee told us that he had checked and he thought his models were still new at the time of talking and they would be published on the arxiv tomorrow (1st July, 2008 - the preprint can be found <a href="http://arxiv.org/abs/0806.4977">here</a>). Lee showed us how to introduce a twisted hypermultiplet into Gaiotto-Witten theory in order to reproduce the 8 scalars of the Bagger-Lambert work. Hey presto, a new technique for building interesting theories was born. The last talk of the day was given by Niko Jokela from Helsinki on the interesting topic of N-Point Functions in the Rolling Tachyon Background, the arxiv preprint is <a href="http://arxiv.org/abs/0806.1491">here</a>.<br /><br />At the end of the day we had a reception hosted at the Academy of Arts and Sciences, of which <a href="http://en.wikipedia.org/wiki/Robbert_Dijkgraaf">Robert Dijkgraaf</a> is the President. He told us that the academy was actually seven years older than the Netherlands and told a story of his predecessor who was approached by Vladimir Putin at a formal dinner and was greeted with the line "so you are a President too", Dijkgraaf's predecessor replied that "they came in all shapes and sizes".<br /><br />After the reception I spent a nice hour wandering around Amsterdam in the sun.Paul Cookhttps://plus.google.com/110983481653378694769noreply@blogger.com37tag:blogger.com,1999:blog-8759090.post-41270400827978651082008-05-30T19:28:00.006+00:002008-05-31T11:08:01.700+00:00So it goes...Well, that's how long a year-a-half is. What did I miss?Â <a href="http://www.liegroups.org/AIM_E8/technicaldetails.html">The E8 genome was mapped</a>Â with the fanfare ofÂ <a href="http://www.math.columbia.edu/~woit/wordpress/?p=534">a press conference</a>, the string wars continued, <a href="http://arxiv.org/abs/hep-th/0611086">N=8 supergravity may be ultraviolet finite</a>Â (also s<a href="http://arxiv.org/abs/hep-th/0611273">ee the argument via string theory properties</a>) if a <a href="http://arxiv.org/abs/0802.0868">no triangle hypothesis</a> holds, funding wasÂ <a href="http://cosmicvariance.com/2007/12/11/uk-physics-investment-decimated/">decimated</a>/<a href="http://cosmicvariance.com/2007/12/19/2008-is-looking-bleak/">bleak</a>/<a href="http://cosmicvariance.com/2008/05/27/downsizing-the-downsizing-at-fermilab/">downsized</a>, <a href="http://arxiv.org/abs/hep-ph/0703260">unparticles</a> were cool, low dimension supergravity was maximally gauged <a href="http://arxiv.org/abs/0712.1795">here</a>, <a href="http://arxiv.org/abs/0711.2035">here</a> and <a href="http://arxiv.org/abs/0705.2101">here</a>,Â <a href="http://arxiv.org/abs/0711.0955">the multiple M2 brane revolution began</a>,Â <a href="http://arxiv.org/abs/0711.0770">an exceptionally simple theory of everything</a>Â was the most popular paper on the arxiv,Â <a href="http://www.amazon.com/String-Theory-M-Theory-Modern-Introduction/dp/0521860695">BeckerBeckerSchwarz</a>Â appeared, Fields medallists blogged en masse (<a href="http://terrytao.wordpress.com/">Tao</a>,Â <a href="http://noncommutativegeometry.blogspot.com/">Connes</a>,Â <a href="http://borcherds.wordpress.com/">Borcherds</a>),Â <a href="http://motls.blogspot.com/2007/03/panel-michael-duff-and-lee-smolin.html">Mike Duff discussed string theory with Lee Smolin</a>,Â <a href="http://www.physics.harvard.edu/about/Phys253.html">Sidney Coleman gave lecturesÂ </a>from the past,Â <a href="http://uk.youtube.com/watch?v=jd1tgLQg4ZU">Stephen Hawking's acquired his own universe</a>, theÂ <a href="http://arxiv.org/find/grp_physics/1/co:+AND+Theory+AND+String+AND+Birth+of/0/1/0/all/0/1">birth of string theory</a>Â was chronicled, John Schwarz also shared hisÂ <a href="http://arxiv.org/abs/0708.1917">memories of early days</a>, Murray Gell-Mann was videoed talking aboutÂ <a href="http://www.ted.com/index.php/talks/view/id/194">beauty in physics</a>,Â <a href="http://uk.youtube.com/watch?v=knDXAr4ltMA&feature=PlayList&p=856EE31881996E0B&index=0&playnext=1">a Feynman video biography</a>Â surfaced... and so on, and so on without end. Nothing stops while you're away.<div><div><br /></div><div><a href="http://www.nytimes.com/2007/08/27/world/europe/27wess.html?_r=1&oref=slogin">Julius Wess</a>,Â <a href="http://www.nytimes.com/2008/04/14/science/14wheeler.html">John A. Wheeler</a>,Â <a href="http://www.news.harvard.edu/gazette/2007/11.29/15-coleman.html">Sidney Coleman</a>,Â <a href="http://en.wikipedia.org/wiki/J%C3%BCrgen_Ehlers">Jurgen Ehlers</a>Â have all sadly passed away.</div><div><br /></div><div>The fantasy author <a href="http://en.wikipedia.org/wiki/Robert_jordan">Robert Jordan</a> died and won't complete his <a href="http://en.wikipedia.org/wiki/The_Wheel_of_Time">Wheel of Time</a> epic and <a href="http://en.wikipedia.org/wiki/Kurt_Vonnegut">Kurt Vonnegut </a>left his own world-line. So it goes...</div><div><br /></div></div><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://bp2.blogger.com/_PB7-q-qIjgE/SEBs_HIorRI/AAAAAAAAAAM/arCK3utsMog/s1600-h/kurt_vonnegut.png"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;" src="http://bp2.blogger.com/_PB7-q-qIjgE/SEBs_HIorRI/AAAAAAAAAAM/arCK3utsMog/s320/kurt_vonnegut.png" border="0" alt="" id="BLOGGER_PHOTO_ID_5206281000743120146" /></a><div><div style="text-align: left;">So that's a year-and-a-half.<br /></div><div><div style="text-align: center;"><br /></div><div><div><br /></div></div></div></div>Paul Cookhttps://plus.google.com/110983481653378694769noreply@blogger.com9tag:blogger.com,1999:blog-8759090.post-74953318332192905602007-04-18T13:12:00.001+00:002011-01-26T18:38:21.345+00:00Large Volume ScenariosHow does one hope to get most of the standard model out of string theory? Yesterday, Marcus Berg from the Albert Einstein Institute in Potsdam, gave a talk reviewing two scenarios, known by their abbreviations KKLT (for Kachrou, Kallosh, Linde, Trivedi) and LVS (for Large Volume Scenario) . His preference was for the LVS and his arguments were motivated mostly by the practicality of stabalising cycles inside the compact space.<br /><br />In summary, The KKLT scenario is a particular set-up of IIB superstring theory, and was proposed as a way to obtain de Sitter vacua from string theory. This was progressive since it was already known that simply the lowest order terms of Sugra were not enough to construct a de Sitter background. KKLT showed that higher order string theory terms could give rise to such a background. In their model the compactified 6 (real) dimensional Calabi-Yau possesses "Klebanov-Strassler" throats and fluxes F_3, H_3 which are non-parallel. The fluxes stabilise the compact space and the addition of anti-D3 branes and associated instantons permits supersymmetry breaking and the emergence of a Minkowski or de-Sitter background. Due to the belief in a small positive cosmological constant the de-Sitter background existing in string theory is highly desirable.<br /><br />The fluxes in KKLT are used to stabilise the dilaton and hence the string coupling constant, and to stabilise the moduli of the Calabi-Yau space. Marcus Berg gave us a review of how one goes about stabilising such moduli. One begins with ten-dimensional fluxes and a ten-dimensional metric, then upon reduction the part of the kinetic term that exists in the internal space gives rise to potential term in the Lagrangian associated with the moduli appearing through the reduction of the metric. To stabilise the moduli one can minimise the potential term and then find the moduli. The trouble with this, according to Marcus Berg, is that the potential is generically composed of exponentially suppressed terms and linear terms, so that the minimum of the potential occurs only over a very small range of parameters. What's the problem with that? Well simply maybe it is wrongheaded, the correct interpretation may be that a tree-level term is being cancelled against a non-perturbative term in the potential.Paul Cookhttps://plus.google.com/110983481653378694769noreply@blogger.com0tag:blogger.com,1999:blog-8759090.post-33493059589293024932007-02-23T11:15:00.001+00:002011-01-26T18:35:50.437+00:00Gabriele Veneziano's Personal RecollectionDid you know that string theory began in Pisa? So said <a href="http://en.wikipedia.org/wiki/Gabriele_Veneziano">Gabriele Veneziano</a> in the first talk of his <a href="http://www.df.unipi.it/dida/dottorat/Veneziano2007.html">special course on string theory</a> here in Pisa, entitled "The Birth of String Theory: A Personal Recollection". Perhaps he was indulging the audience. Perhaps. He told us that as a graduate student from the University of Florence he came in the Spring of 1966 to listen Sergio Fubini's talks in Pisa and really this was the beginning of the path towards a theory of strings. Of course, at that time string theory was not being proposed as a theory containing gravity but rather as a theory of the strong interactions. Veneziano described working on current algebras and superconvergence relations at the Weizmann Institute in 1966-67 and listening to Murray Gell-Mann's talk at Erice in July 1967 as being important in leading him to a dual resonance model.<br /><br />From Gell-Mann, he learned about Geooffrey Chew's "expensive" bootstrap method for calculating scattering amplitudes. Chew' s bootstrap he said related objects of different types; baryons in the s-channel became mesons in the t-channel. And the rest of the story as they say is history.Paul Cookhttps://plus.google.com/110983481653378694769noreply@blogger.com0tag:blogger.com,1999:blog-8759090.post-1165339055165106262006-12-05T17:11:00.000+00:002006-12-05T17:17:35.196+00:00JHEP Editorial PleaIn my email today, a gentle call to scientists to support JHEP. One must wonder if JHEP is in trouble. Let's hope not. Read on:<br /><br /><blockquote>Dear Colleague,<br /><br />In the first half of 2006 our Journals have seen many important changes: a new instrumentation journal, JINST, has been launched, new scientific directors for JHEP and JCAP have been appointed to replace Hector Rubinstein, now Scientific Advisor to SISSA Medialab. We wish to remind you of the basic differences between our not-for-profit Journals and those published by commercial publishing companies.<br /><br />The policy of the SISSA-IOP J-Journals is the following:<br />- to maintain the philosophy that publication of research results must be fully controlled by scientists, so as to ensure the highest scientific quality;<br />- to produce information efficiently at a reasonable cost, thereby minimizing the financial pressure on our libraries and grants.<br /><br />We are convinced that it is unfair that publishing companies make huge profits exploiting the ingenuousness of scientists in the questions related with the publication of their own results in Scientific Journals. Although scientists voluntarily carry out all the publication-related work (starting with the actual writing of the paper to the peer-review), they are still requested to pay unwarranted<br />and outrageous subscription fees by commercial publishing companies for them to access these very journals as readers.<br /><br />Here are some examples. The yearly subscription cost of our journals, which covers only necessary expenses unavoidably related with publication and marketing of all published scientific contributions, are the following:<br /><br />JHEP: EUR 1,622<br />JCAP: EUR 1,174<br />JINST (free in 2006): 745 in 2007<br />(all institutional prices)<br /><br />The sum of the subscriptions to Nuclear Physics B and Physics Letters B is more than fifteen times higher than that of JHEP (to which the combined NPB + PLB can be compared), i.e., 15,211 EUR (Institutional price) plus 10,301 EUR (Institutional price) = 25,512 EUR. In Instrumentation, JINST's main competitor, Nuclear Instruments and Methods A, charges as an annual subscription fee 12,191 EUR (Institutional price).<br /><br />Exploiting this strategy, commercial publishing companies have managed to generate profits of the order of one billion euros a year(Elsevier), which are ultimately taken from research resources.<br /><br />Besides being run and published entirely by electronic means, the other key features of our journals are:<br /><br />1. The Editor-in-Charge is given full responsibility for acceptance or rejection of the paper. His word is final and cannot be questioned by the Editorial Office (on the other hand, authors can appeal against editorial decisions). This has proved to be very efficient in selecting papers of very high quality and consequently Thompson ISI's impact factors for JCAP and JHEP are amongst the highest in physics<br />(JINST started publication this year so it is not rated yet). Please see the data appended below.<br /><br />2. Large companies misuse the copyright assignment, forbidding authors to use their own material when they need to do so, e.g., for publishing collected reprints. They have done it in the past, based on non-scientific considerations. We do not. Indeed unlike those of commercial publishers our policies are never in conflict with scientific interests because science is our only concern.<br /><br />We very much rely on your support and we would appreciate it if you could contribute by conveying to colleagues the information above and encouraging those who have not yet done so to submit their results to our journals.<br /><br />We do believe that there should not be any monopoly of publication. The existence of several journals (hopefully in the future all not-for-profit enterprises), protects the author against the possibility that if a mistake is made the paper cannot be<br />published. Furthermore, we see no reason why large companies involved in media, newspapers and other matters should have such control of scientific research to which they contribute nothing.<br /><br />Is it up to all of us, and up to you as an author in particular, to stop this unacceptable state of affairs.<br /><br />Sincerely yours,<br /><br />Marc Henneaux - Scientific Director<br />Hector Rubinstein - Scientific Advisor<br /><br />IF data<br /><br />(We are fully aware that Impact Factors are far from being absolute measures of quality and can be, for instance, influenced by fashion effects. IFs give only a partial indication. The data below are thus to be taken with a grain of salt)<br /><br />Journal IF 2003 IF 2004 IF 2005<br /><br />JHEP 6.854 6.503 5.944<br />Physical Review D 4.358 5.156 4.852<br />Nuclear Physiscs B 5.409 5.819 5.522<br />Physics Letter B 4.298 4.619 5.301<br />Euro Phy J C 6.162 3.209<br /><br />JCAP 7.914 6.793<br />A & A 3.781 3.694 4.223<br />Class and Quant Grav 2.107 2.941 2.938<br />Astrophysical Journal 6.187 6.237 6.308<br />inter J Mod Phys D 1.507 1.500 1.225</blockquote>Paul Cookhttps://plus.google.com/110983481653378694769noreply@blogger.com11tag:blogger.com,1999:blog-8759090.post-1163019019192597872006-11-08T20:26:00.000+00:002006-11-08T20:54:35.123+00:00Lisa Randall Online!Just a short note to let you know that <a href="http://en.wikipedia.org/wiki/Lisa_Randall">Lisa Randall</a>, <a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://photos1.blogger.com/blogger/1292/610/1600/Lisa-randall-at-ted.jpg"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;" src="http://photos1.blogger.com/blogger/1292/610/320/Lisa-randall-at-ted.jpg" border="0" alt="" /></a>will be online tomorrow (Thursday 8th Novermber, 2006) for an open <a href="http://www.discover.com/web-exclusives/lisa-randall-online-chat/">discussion about physics</a>, strings, <a href="http://www.amazon.co.uk/Warped-Passages-Unravelling-Universes-Dimensions/dp/0713996994/sr=8-2/qid=1163018326/ref=sr_1_2/202-7109632-7820614?ie=UTF8&s=books">Warped Passages</a> and <a href="http://en.wikipedia.org/wiki/Randall-Sundrum">how to create your own universe</a> (presumably). The event is being run by <a href="http://en.wikipedia.org/wiki/Discover_magazine">Discover magazine</a>, and to whet your appetite you can read an interview with Lisa from Discover earlier this year <a href="http://www.discover.com/issues/jul-06/features/interview-randall/">here</a>. I don't know exactly what you have to do to be involved but presumably turn up at <a href="http://www.discover.com/">Discover magazine's site</a> from 2pm until 3pm (in the reference frame of the eastern shore of the US) be dressed in your finest surfing gear (the web kind, anything else would be surreal wouldn't it?), bring a question and a bottle. Why not?<br /><br /><span style="font-style:italic;">Thanks to Coco Ballantyne for the head's up.</span>Paul Cookhttps://plus.google.com/110983481653378694769noreply@blogger.com2tag:blogger.com,1999:blog-8759090.post-1158065931993813602006-09-12T19:54:00.000+00:002006-09-12T19:00:13.936+00:00A Penrose UniverseFirst, there have been a number of introductory posts on the Barrett-Connes standard model spectral triple over at the n-category cafe, in particular see posts <a href="http://golem.ph.utexas.edu/category/2006/09/connes_on_spectral_geometry_of.html">I</a>, <a href="http://golem.ph.utexas.edu/category/2006/09/connes_on_spectral_geometry_of_1.html">II</a>, <a href="http://golem.ph.utexas.edu/category/2006/09/connes_on_spectral_geometry_of_2.html">III</a> and <a href="http://golem.ph.utexas.edu/category/2006/09/connes_on_spectral_geometry_of_3.html">IV</a>. Second John Barrett has been talking about his approach to finding the appropriate spectral triple in Cambridge yesterday, his paper, "<a href="http://arxiv.org/abs/hep-th/0608221">A Lorentzian version of the non-commutative geometry of the standard model of particle physics</a>" appeared on the arxiv on the same day as Connes' and suggested identical alterations, and while I have been feverishly attacking my thesis, Alejandro Rivero attended the talk and has made some comments about it on <a href="http://www.physicsforums.com/showthread.php?t=125767">physics forums</a>. He also has uploaded his <a href="http://www.flickr.com/photos/72166458@N00/241378310/">notes</a> from the talk, but these are a little hard to read. Also the <a href="http://www.newton.cam.ac.uk/">Newton Institute</a> have audio of all the talks from last week's workshop for you to enjoy <a href="http://www.newton.cam.ac.uk/webseminars/pg+ws/2006/ncg/ncgw02/">here</a>. <br /><br />On a different note, a while ago I attended the <a href="http://www.lnf.infn.it/~bellucci/SAM2006.html">Winter School on the Attractor Mechanism</a> in Frascati but was unable to write up much about it due to being very busy. Well <a href="http://personnel.physics.ucla.edu/directory/faculty/index.php?f_name=kraus">Per Kraus</a>, who gave a set of talks at the school has helped me out by publishing his lecture notes on the archive as <a href="http://arxiv.org/abs/hep-th/0609074">"Lectures on black holes and the AdS3/ CFT2 correspondence"</a>. Thank-you Per!<br /><br />You have probably heard of <a href="http://en.wikipedia.org/wiki/Penrose_tiling">Penrose tilings</a>, <a href="http://en.wikipedia.org/wiki/Penrose_diagram">Penrose diagrams</a>, <a href="http://www.maths.ed.ac.uk/~hannu/EMPG.pdf#search=%22penrose%20limit%22">Penrose limits</a>, <a href="http://en.wikipedia.org/wiki/Penrose_triangle">Penrose triangles</a> and even a <a href="http://en.wikipedia.org/wiki/Penrose_stairs">Penrose staircase</a>, well last week, during <a href="http://en.wikipedia.org/wiki/Roger_Penrose">Roger Penrose</a>'s talk at the <a href="http://www.newton.cam.ac.uk/programmes/NCG/ncgw02">Noncommutative Geometry Workshop</a>, I heard a little about a Penrose Universe. (In my picture it looks like Roger Penrose is keeping the audience entertained with his shadow puppet routine)<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://photos1.blogger.com/blogger/1292/610/1600/Penrose.jpg"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;" src="http://photos1.blogger.com/blogger/1292/610/320/Penrose.jpg" border="0" alt="" /></a>It is a peculiar thing and represents Penrose's approach to understanding the second law of thermodynamics, that entropy increases, on a cosmological scale. Penrose points out that there is a contradiction in the entropy increase picture of the big bang, which is that the background radiation matches a model that is in thermal equilibrium. Such a state is just about the highest entropy state you can imagine for a system. Almost any other distribution besides uniform would result in a smaller entropy. The Big Bang picture requires the restriction of phase space at early time and the consequence that entropy ought to be tiny at the Big Bang. Penrose wonders how to resolve this contradiction, and seeks to resolve it by separating the entropy of the universe into that arising from matter (the eneergy momentum tensor) and that encoded in gravitational degrees of freedom (the Weyl curvature, see below).<br /><br />In a nutshell it is a universe without a big crunch, and if taken to the extreme limit without a big bang, but which gives the features of energy density fluctuations in the background radiation. Penrose suggested his <a href="http://en.wikipedia.org/wiki/Weyl_curvature_hypothesis">Weyl curvature hypothesis</a> in 1979 as a physical origin of the increasing entropy of the universe with time. The <a href="http://en.wikipedia.org/wiki/Weyl_curvature">Weyl curvature tensor</a> is the traceless part of the Riemann curvature, i.e. the parts which when contracted upon two indices give zero for the Ricci (two-form) tensor. To quote Penrose's description, <blockquote>"In Einsteinâ€™s theory the Ricci curvature R_{ab} is directly determined by the gravitational sources, via the energy-momentum tensor of matter (analogue of the charge-current vector J_{a} in Maxwellâ€™s electromagnetic theory) and the remaining part of the space-time Riemann curvature, namely the Weyl curvature C_{abcd}, describes gravitational degrees of freedom (analogue of the field tensor F_{ab} of Maxwellâ€™s theory)."</blockquote>The Weyl curvature hypothesis is that the Weyl curvature is zero at the big bang but rises gradually as the universe ages. Consequently the Weyl curvature will not be zero at black hole singularities and we may use the Weyl curvature in this picture to distinguish between cosmological singularities and other singularities. As time passes, the Weyl curvature increases and gravitational masses attract each other more strongly forming a less-homogeneous universe, with clumped masses and higher entropy encoded in the dense packing massive bodies. So that early uniform universe may be explained by there being zero Weyl curvature. Penrose talks about the Weyl curvature's growth as freeing up gravitational degrees of freedom that may then be excited. It is the excitation of these gravitaional degrees of freedom that is the real measure of entropy. It is a nice picture. But just what drives the Weyl curvature's variance is a mystery to me. It does allow us to describe gravitational entropy increase with a tensor field, and of course to associate the arrow of time with such a field. So, at least, algebraically it is appealing. It also offers an alternative to a fast period of inflation in the early universe, which some might find equally as arbitrary as a varying curvature field.<br /><br />The latest idea is built upon the findings of Paul Tod in his paper "<a href="http://arxiv.org/abs/gr-qc/0209071">Isotropic cosmological singularities: other matter models</a>", where it is shown that even though the Ricci curvature blows up at the cosmological singularity the Weyl curvature remains finite. Penrose takes this finding and argues that near the big bang gravity becomes a conformal theory, so that he may rescale the metric to infinity and blow up the big bang singularity. The justification for this is that near the big bang, when temperatures are extremely high, there is little difference between the dynamics of massive and massless particles, all particles are treated as massless, and respect conformal equations of motion. Once the description of physics is conformally invariant, Penrose says that a sense of time is lost, tying in neatly with the low entropy ideas. Having blown-up the cosmological singularity, and beleiving that the Weyl curvature remains finite, has lead Penrose to ponder the smooth continuation of the Weyl curvature at the boundary. Perhaps, he suggests, in what he refers to as his "outrageous" proposal, there is a "conformal cyclic cosmology", in which one may knit the conformal geometry at the big bang to another conformal geometry prior to the big crunch, and thereby create a series of universes with a long-lived/eternal conformal geometry. <br /><br />How can Penrose convince us that geometry may become conformal again at the end of the universe's lifetime? Well, he says, after most of the matter in the universe has been swallowed by black holes and has then been recycled back into the universe via massless Hawking radiation we are really only troubled by charged matter that escaped this process. Here we must presume that black holes can radiate away to pure radiation (which seems unlikely - no topology change, no unexcited microstates...) leaving a universe that may contain some unabsorbed charged matter (let's call all matter electrons) and photons. Now if we can come up with some way of doing away with the electrons, says Penrose, then we will be in business. For again without any massive particles left in the universe the scale of the metric has lost its meaning. This is the real weak point, since the mechanisms to get rid of electrons require either allowing their charge or their mass to dissipate over long time scales. But, of course, this may be possible. Once this position is arrived at one might imagine a conformal rescaling of the metric down to zero, so that a future infinite region is made finite and may be attached to the finite cosmological singularity of some other universe. Penrose argues that the appropriate conformally invariant verion of general relativity the spin-2 field picks up an inverse conformal factor when the conformal tranformation is applied to the metrc, while the Weyl curvature does not. Hence the matter density from the previous universe survives the conformal rescaling and passes over into the next universe. Penrose identifies this with the density fluctuations at the Big Bang - which is exceedingly appealing, and presumably testable. <br /><br />The conformal rescaling marks the beginning of the "new" universe. In this picture there is also cosmological scale clock, whose ticks are the rescalings of the metric, so nothing to worry about on a local level. It is also imperitive that the conformal rescalings occur in the right way, i.e. to infinity at big bang singularity and to zero at late time. Effectively one must imagine that the previous universe occured at miniture scale comparatively, and the future universe will be built upon the swirling dust of ours at a gigantic scale. It doubles as a very nice picture for a science-fiction novel, as well as an exceedingly interesting proposal for the origin of the density fluctuations in the universe.<br /><br />We have mentioned the assumptions, namely that black holes evaporate to pure radiation and that electron charge/mass dissipates. There are also questions about particle antiparticle pair creation, but which if we are able to argue in favour of some long term alteration of the properties of the electron, so that it eventually becomes pure radiation, this would not present a problem. Furthermore there seem to be mysterious forces driving the rescaling of the metric, for which it would seem some additional dilaton field may be necessary or some other argument presented. <br /><br />You can hear Penrose talk on this in two places on the web, both of which took place at the Newton Institute. The first is from <a href="http://www.newton.cam.ac.uk/webseminars/pg+ws/2005/gmr/gmrw04/1107/penrose/">November 2005</a> at the <a href="http://www.newton.cam.ac.uk/webseminars/pg+ws/2005/gmr/gmrw04/">Spitalfield's Day</a> and the second occurred <a href="http://www.newton.cam.ac.uk/webseminars/pg+ws/2006/ncg/ncgw02/0906/penrose/">last <br />week</a> (you will have to wait until the end to hear about this cosmological model). Penrose also has written up his description of wha he refers to as "conformal cyclic cosmology" in the proceedings of the EPAC, 2006, conference, and one can read the pdf <a href="http://accelconf.web.cern.ch/accelconf/e06/PAPERS/THESPA01.PDF#search=%22roger%20penrose%20conformal%20gravity%20cosmology%20%22EPAC%22%22">here</a>. <br /><br />On Thursday of last week we also suffered a panel discussion on the nature of space-time, being organised by the sponsors the notorious Templeton foundation, I was a little wary. I think on the whole the event worked very well, it was simply not to <a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://photos1.blogger.com/blogger/1292/610/1600/Panel.jpg"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;" src="http://photos1.blogger.com/blogger/1292/610/320/Panel.jpg" border="0" alt="" /></a>my personal taste, but I went along to enjoy the views of (Rev. Dr.)John Polkinghorne(Eclesiastical physicist), (Prof.) Shahn Majid, (Rev. Dr.) Michael Heller (of the Vatican observatory), (Sir) Roger Penrose and (Prof.) Alain Connes. As you might imagine there was a very strong representation of the religious apprecatiation of spacetime, and even Alain Connes couldn't resist talking of his interpretation of three pages of "ancient text" by which he meant the Veltman Lagrangian of the standard model. I do not think it was a night of much scientific progress. But there were some anecdotal highlights. The evening was organised so that each panelist took five minutes to mention their conception of spacetime, there was an overhead projector and it appeared that the speakers were well organised having prepared detailed slides. Throughout the first two talks Alain Connes looked a little preoccupied, occasionally staring at the desk and sometmes laying his head upon it. Suddenly after the second speaker Connes sprang to life, borrowed some OHP slides and multicoloured pens from the others, and began to prepare his own slides there and then. Since the chairman was supposedly inviting the presentations at random this seemed a wonderfully carefree approach. It made for some nice theatre. We also heard an anecdote from Roger Penrose, in response to the first question from the audience which was along the lines of 'which came first quantum mechanics or general relativity?'. Penrose replied by telling of a time he had listened to a wonderfully animated lecture by John Wheeler and at the end there came a similar question from the audience, which came first G.R. or the quantum principle? Penrose said that a small voice in the front of the audience piped up and asked 'what is the quantum principle?' The small voice belonged to Dirac. A final amusing interchange involved Shahn Majid, the chairman (Jeremy Butterfield) and a mischievous Alain Connes. Shahn Majid was summing up his disenchantment with the present understanding of spacetime with the Shakespearean line "there is something rotten in the state of Denmark" (Penrose said later he thought Majid was referring to the Copenhagen interpretation), and Alain Connes responded with another Shakespeare quotation "Throw physics to the dogs; I'll none of it." It was left to Jeremy Butterfield to point out that the actual line from Macbeth is about "physic" (referring to medecine) and not "physics". So there was some enjoyment to be had from the evening after all.Paul Cookhttps://plus.google.com/110983481653378694769noreply@blogger.com56tag:blogger.com,1999:blog-8759090.post-1157366540812590082006-09-04T23:24:00.000+00:002006-09-04T22:29:15.123+00:00To Commute or not to Commute...<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://photos1.blogger.com/blogger/1292/610/1600/Isaac%20Newton%20Institute%20in%20Cambridge.jpg"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;" src="http://photos1.blogger.com/blogger/1292/610/320/Isaac%20Newton%20Institute%20in%20Cambridge.jpg" border="0" alt="" /></a> Sorry for the lack of posting this summer, but I have been trying to write up my thesis. In fact I still am trying, and for no sensible reason I am now doing this at the Noncommutative Geometry Workshop at The <a href="http://www.newton.cam.ac.uk/">Isaac Newton Institute for Mathematical Sciences</a> in <a href="http://www.cam.ac.uk/">Cambridge</a>. The institute is a wonderful place, although I haven't looked around much I have already heard about the lawn on the roof (where you can sometimes see someone mowing, which must look very peculiar from the road) and seen the bust of Paul Dirac in the foyer. But I have been most impressed by the blackboard which is mounted in the lavatory<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://photos1.blogger.com/blogger/1292/610/1600/blackboard%20in%20the%20toilets.jpg"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;" src="http://photos1.blogger.com/blogger/1292/610/320/blackboard%20in%20the%20toilets.jpg" border="0" alt="" /></a>, should you have a maths dispute in the bathroom - it is by far the geekiest thing I have ever seen. It is wonderful and then horrifying and finally wonderful again.<br /><br />It is also very nice to be visting Cambridge again, and King's College looked especially pretty today in the sunshine. I refer you to my picture below (see there was sunshine today!) <br /><br />The <a href="http://www.newton.cam.ac.uk/programmes/NCG/ncgw02p.html">programme is available online</a> and today was the first day of five days of talks. There's also a public debate on thursday at 8pm in Queen's Lecture Theatre at Emmanuel College entitled "<a href="http://www.newton.cam.ac.uk/programmes/NCG/ncgw02_pd">The Nature of Space and Time: An Evening of Speculation</a>" invoving a panel of Alain Connes, Roger Penrose, Shahn Mahjid, Michael Heller and John Polkinghorne which should be interesting. If you are in Cambridge and want to come along you might benefit from registering at the above link. Or maybe you won't benefit - it is not clear. <a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://photos1.blogger.com/blogger/1292/610/1600/King%27s%20College%20from%20the%20back.jpg"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;" src="http://photos1.blogger.com/blogger/1292/610/320/King%27s%20College%20from%20the%20back.jpg" border="0" alt="" /></a><br /><br /><br />The first talk this morning was "<a href="http://www.newton.cam.ac.uk/programmes/NCG/abstract2/rivasseau.html">The Quest for Non Commutative Field Theory</a>" by <a href="http://cpth.polytechnique.fr/cpth/rivass/rivasseng.html">Vincent Rivasseau</a> and we heard about noncommutative field theory in review. The talk began with a reminder about why noncommutative geometry is an interesting approach to quantum gravity, it went like this: <blockquote>Quamtum Mechanics (Non commutativity) + General Relativity (Geometry) = Non commutative geometry.<br /></blockquote> Noncommutative field theory is the generalisation of well-known quantum field theories such as the phi^4 theory to noncommutative spacetimes. The approach is to upgrade the normal scalar product to the simplest non-commutative product which is known as the Moyal product and denoted by an asterisk. One can read all about this in a review paper from 2001 by Michael Douglas and Nikita Nekrasov called, you guessed it, "<a href="http://www.arxiv.org/abs/hep-th/0106048">Noncommutative Field Theory</a>". Rivasseau described the problems of renormalisations of such a naive upgrade to noncommutative geometry, while the planar Feynman diagrams and their ultra-violet divergence remain renormaliazable the non-planar ones pick up an infra-red divergence. This goes by the name of UV/IR mixing and some more complicated terms are needed before the noncommutative version of the theory can be made renormalizable. See <a href="http://arxiv.org/abs/hep-th/0512271">Rivasseau's paper with Gurau, Magnen and Vignes-Tourneret</a> for the detail on the renormalizability of noncommuting phi^4 field theory. We were also introduced to the modifications of the Feynman diagrams resulting from the noncommutative promotion. In the commuting field theory one uses the heat kernel as the propagator, while in noncommutative geometry the Mehler Kernel (which is far more complicated than the heat kernel) is the starting point. Interactions, which we are used to describing by one spacetime point, become dependent upon four and a vertex is promoted to a box, the four points specifying the corners. Rivasseau et al also have a paper entitled "<a href="http://arxiv.org/abs/hep-th/0512071">Propagators for Noncommutative Field Theories</a>". The end of the talk was dedicated to the parametric space which is a new approach to noncommuative field theory described by Gurau and Rivasseau in their <a href="http://arxiv.org/abs/math-ph/0606030">paper</a>. Since I am trying to get a small understanding of the tools used in noncommutative geometry and the motivations I would like to mention a couple of recurrent topics, whose importance I was unable to understand during the talk. The first is that the quantum hall effect seems to be a very important physical example cited by the noncommutative geometers. The second tool that was apparently of great practical value is the so-called Langmann-Szabo duality, which I think was introduced in their paper "<a href="http://arxiv.org/abs/hep-th/0202039">Duality in Scalar Field Theory on Noncommutative Phase Spaces</a>".<br /><br />At 11.35pm <a href="http://www.math.ucdavis.edu/~schwarz/">Albert Schwarz</a> began talking to us under the title "<a href="http://www.newton.cam.ac.uk/programmes/NCG/abstract2/schwarz.html">Space and Time from Translation Symmetry</a>". The talk followed very closely his <a href="http://arxiv.org/abs/hep-th/0601035">paper of the same title</a>. He did not talk about noncommutativity much but gave us an axiomatic description of quantum mechanics as a unital, associative algebra of observables, A, over the complex space. He described translations as acting as automorphisms of the algebra A, and soon generalized the idea of a tranlsation generator to a commutative subalgebra. He said he was not trying to give solutions but rather to formulate problems. Alain Connes was interacting with Schwarz from the front row and at one point Connes asked repeatedly about the observables of string theory, culminating with "...but what are the observables?" To which Schwarz replied "There is no question: 'what is observables?'". It was rather like a Jedi mind trick. Schwarz expressed a strong interest in the notion that all physical numbers should be rational, while anything else is just used for felicity. He advocated using p-adic numbers instead of real numbers and the functioning of this proposal can be read about in his recent papers with Kontsevich, Vologodsky and Shapiro [<a href="http://arxiv.org/abs/hep-th/0603106">1</a> and <a href="http://arxiv.org/abs/hep-th/0606151">2</a>].<br /><br />After lunch, <a href="http://www.maths.tcd.ie/people/index.php?file=people&code=SSh">Samson Shatashvili</a> talked under the title "Higgs bundles, gauge theories and quantum groups" who described his reasons for claiming that the so-called Yang-Mills-Higgs theories are dual to the nonlinear Schrodinger quantum system. The preprint (with A. Gevasinov) that the talk was based on is due to appear overnight at <a href="http://www.arxiv.org/abs/hep-th/0609024">hep-th/0609024</a>, but a fundamental paper in the literature, at almost ten years of age, is "<a href="http://arxiv.org/abs/hep-th/9712241">Integrating Over Higgs Branches</a>" by Greg Moore, Nikita Nekrasov and Shatashvili. At the end of his talk Shatashvili made the point that as far as he could tell his dual theories contained all the information required for geometric Langlands duality (although he also claimed to not know what geometric Langlands is) and both regimes of the duality are reasonably well understood. But I think we'll have to wait for the preprint...<br /><br />Today's final talk was a big one. The speaker was the wonderful <a href="http://www.alainconnes.org/">Alain Connes</a> and he was talking about his recent short paper describing a theory of everything. Lubos Motl has commented extensively on this preprint which you can read by boosting to his <a href="http://motls.blogspot.com/2006/08/alain-connes-theory-of-everything.html">Reference Frame</a>. You can also read Alain Connes explanation of himself in the preprint, "<a href="http://arxiv.org/abs/hep-th/0608226">Noncommutative Geometry and the Standard Model with Neutrino Mixing</a>" but it will take a lot of work if you are of a more physical than mathematical constitution. Connes described his aim to encode the gravitational and the standard model Lagrangian in a purely geometric picture. The essence of the approach is not to use the metric to define the square of the line element, but rather to start with the line element, and not its square, by using the Dirac operator, D. In fact ds = 1/D. This approach was used to construct the standard model via the spectral action principle in work with Ali Chamseddine (see [<a href="http://arxiv.org/abs/hep-th/9603053">1</a>,<a href="http://arxiv.org/abs/hep-th/9606001">2</a>]. However the resulting theory was not able to match the standard model perfectly, it exhibited fermion doubling (as pointed out in the work of <a href="http://arxiv.org/abs/hep-th/9610035">Lizzi, Mangano, Miele and Sparano</a>) and the introduction of right-handed neutrinos caused Poincare duality to be violated. In his latest work Connes has fixed the problems and reproduced the standard model Lagrangian. This is no mean feat, at the beginning of his talk Connes bamboozled the audience by displaying the enormous Lagrangian of the standard model as written down by Veltman. It filled one page of A4 (single-spaced) and no-one in the audience could read it clearly. In Connes latest work one takes what is called the "finite space", F, of the standard model algebra which is 90-dimensional corresponding to 45 particles and 45 antiparticles. One then writes down the spectral action which has two terms, one for bosons and one for fermions, and one feeds in the spectral dimension....wait! What's the spectral dimension??? Well apparently this is the sequence of positive integers bounded above, and specified, by the metric dimension - and the metric dimension is our usual notion of dimension. There is also another type of dimension called the KO-dimension coming from K-theory, which I do not claim to understand, but Connes' fix of his theory involves allowing the metric dimension to take different values to the KO-dimension. In particular the conjugation properties of the relevant spinors and the necessity of removing his double fermions leads to picking the KO-dimension of the required space F, which Lubos has taken to calling the Connes manifold, to be 6mod8. From our experience of spacetime the metric dimension is 4 and in total the dimension of MxF becomes 10mod8 - which are dimensions that are exceedingly familiar from string theory. Connes strongly denied suggestions that his finite space F was anything like a Calabi-Yau manifold, but said that if someone showed that it was, then he would applaud. Having made these changes to the spectral dimension data that is fed into the spectral action formulation, Connes told us that he expanded out the explicit action and exactly reproduced the enormous Veltman Lagrangian. Due to the compactness of the notation this is an extremely elegent construction of the standard model, and while it may not answer the questions about why certain data are fed in, it is certainly a remarkable discovery. No doubt there is more to be uncovered along these lines. Connes told us that the preprint on the archive is a short version of a much more detailed paper to appear later on, again with Chamseddine. At the end of the talk Connes told the audience that the finiteness of the space F is really tantamount to there existing a basic unit of length, and it was revealed during the questions that it was really the Euclidean version of the standard model that had been constructed. Nevertheless the compact notation makes this approach worth some study. <br /><br />It is clear to me after today that I wouldn't win the Krypton Factor challenge for observation: I have been surrounded by the words "noncommutative", "non commutative" and "non-commutative" and I still haven't worked out which is the officially endorsed spelling (see my non-renormalized spellings in the text). To hyphen or not to hyphen...that is really the question?Paul Cookhttps://plus.google.com/110983481653378694769noreply@blogger.com14tag:blogger.com,1999:blog-8759090.post-1154816991379836162006-08-05T23:24:00.000+00:002006-08-05T22:32:09.480+00:00Physics: More damaging than drugs?I just had this advice entitled unequivocally "<a href="http://www.physics.wustl.edu/~katz/scientist.html">Don't Become a Scientist!</a>" taken from <a href="http://www.physics.wustl.edu/~katz/">Jonathan I. Katz's website</a> forwarded to me by a friend (who quit physics to work in the financial sector) - I wouldn't have thought it to be of general interest, but apparently it is interesting enough to become a forwarded email in certain circles. It is, of course, of interest here, where all advice to young researchers from one's elders is welcome, no matter how terrifying :( - it has been discussed elsewhere over a year-and-a-half ago by <a href="http://duende.uoregon.edu/">Stephen Hsu</a> (<a href="http://infoproc.blogspot.com/2004/12/dont-become-scientist.html">part 1</a> and <a href="http://infoproc.blogspot.com/2005/09/dont-become-scientist-ii.html">part 2</a>) at his blog, <a href="http://infoproc.blogspot.com/">Information Processing</a>, and also at <a href="http://cosmicvariance.com/sean">Sean Carroll's</a> former blog incarnation, <a href="http://preposterousuniverse.blogspot.com/">Preposterous Universe</a>, <a href="http://preposterousuniverse.blogspot.com/2005_01_01_preposterousuniverse_archive.html"> (see 5th January, 2005)</a> and there were some comments on it by the <a href="http://dabacon.org/pontiff/?p=765">Quantum Pontiff</a> as well, but perhaps, like me, you missed this before:<br /><br />"Are you thinking of becoming a scientist? Do you want to uncover the mysteries of nature, perform experiments or carry out calculations to learn how the world works? Forget it!<br /><br />Science is fun and exciting. The thrill of discovery is unique. If you are smart, ambitious and hard working you should major in science as an undergraduate. But that is as far as you should take it. After graduation, you will have to deal with the real world. That means that you should not even consider going to graduate school in science. Do something else instead: medical school, law school, computers or engineering, or something else which appeals to you.<br /><br />Why am I (a tenured professor of physics) trying to discourage you from following a career path which was successful for me? Because times have changed (I received my Ph.D. in 1973, and tenure in 1976). American science no longer offers a reasonable career path. If you go to graduate school in science it is in the expectation of spending your working life doing scientific research, using your ingenuity and curiosity to solve important and interesting problems. You will almost certainly be disappointed, probably when it is too late to choose another career.<br /><br />American universities train roughly twice as many Ph.D.s as there are jobs for them. When something, or someone, is a glut on the market, the price drops. In the case of Ph.D. scientists, the reduction in price takes the form of many years spent in ``holding pattern'' postdoctoral jobs. Permanent jobs don't pay much less than they used to, but instead of obtaining a real job two years after the Ph.D. (as was typical 25 years ago) most young scientists spend five, ten, or more years as postdocs. They have no prospect of permanent employment and often must obtain a new postdoctoral position and move every two years. For many more details consult the Young Scientists' Network or read the account in the May, 2001 issue of the Washington Monthly.<br /><br />As examples, consider two of the leading candidates for a recent Assistant Professorship in my department. One was 37, ten years out of graduate school (he didn't get the job). The leading candidate, whom everyone thinks is brilliant, was 35, seven years out of graduate school. Only then was he offered his first permanent job (that's not tenure, just the possibility of it six years later, and a step off the treadmill of looking for a new job every two years). The latest example is a 39 year old candidate for another Assistant Professorship; he has published 35 papers. In contrast, a doctor typically enters private practice at 29, a lawyer at 25 and makes partner at 31, and a computer scientist with a Ph.D. has a very good job at 27 (computer science and engineering are the few fields in which industrial demand makes it sensible to get a Ph.D.). Anyone with the intelligence, ambition and willingness to work hard to succeed in science can also succeed in any of these other professions.<br /><br />Typical postdoctoral salaries begin at $27,000 annually in the biological sciences and about $35,000 in the physical sciences (graduate student stipends are less than half these figures). Can you support a family on that income? It suffices for a young couple in a small apartment, though I know of one physicist whose wife left him because she was tired of repeatedly moving with little prospect of settling down. When you are in your thirties you will need more: a house in a good school district and all the other necessities of ordinary middle class life. Science is a profession, not a religious vocation, and does not justify an oath of poverty or celibacy.<br /><br />Of course, you don't go into science to get rich. So you choose not to go to medical or law school, even though a doctor or lawyer typically earns two to three times as much as a scientist (one lucky enough to have a good senior-level job). I made that choice too. I became a scientist in order to have the freedom to work on problems which interest me. But you probably won't get that freedom. As a postdoc you will work on someone else's ideas, and may be treated as a technician rather than as an independent collaborator. Eventually, you will probably be squeezed out of science entirely. You can get a fine job as a computer programmer, but why not do this at 22, rather than putting up with a decade of misery in the scientific job market first? The longer you spend in science the harder you will find it to leave, and the less attractive you will be to prospective employers in other fields.<br /><br />Perhaps you are so talented that you can beat the postdoc trap; some university (there are hardly any industrial jobs in the physical sciences) will be so impressed with you that you will be hired into a tenure track position two years out of graduate school. Maybe. But the general cheapening of scientific labor means that even the most talented stay on the postdoctoral treadmill for a very long time; consider the job candidates described above. And many who appear to be very talented, with grades and recommendations to match, later find that the competition of research is more difficult, or at least different, and that they must struggle with the rest.<br /><br />Suppose you do eventually obtain a permanent job, perhaps a tenured professorship. The struggle for a job is now replaced by a struggle for grant support, and again there is a glut of scientists. Now you spend your time writing proposals rather than doing research. Worse, because your proposals are judged by your competitors you cannot follow your curiosity, but must spend your effort and talents on anticipating and deflecting criticism rather than on solving the important scientific problems. They're not the same thing: you cannot put your past successes in a proposal, because they are finished work, and your new ideas, however original and clever, are still unproven. It is proverbial that original ideas are the kiss of death for a proposal; because they have not yet been proved to work (after all, that is what you are proposing to do) they can be, and will be, rated poorly. Having achieved the promised land, you find that it is not what you wanted after all.<br /><br />What can be done? The first thing for any young person (which means anyone who does not have a permanent job in science) to do is to pursue another career. This will spare you the misery of disappointed expectations. Young Americans have generally woken up to the bad prospects and absence of a reasonable middle class career path in science and are deserting it. If you haven't yet, then join them. Leave graduate school to people from India and China, for whom the prospects at home are even worse. I have known more people whose lives have been ruined by getting a Ph.D. in physics than by drugs.<br /><br />If you are in a position of leadership in science then you should try to persuade the funding agencies to train fewer Ph.D.s. The glut of scientists is entirely the consequence of funding policies (almost all graduate education is paid for by federal grants). The funding agencies are bemoaning the scarcity of young people interested in science when they themselves caused this scarcity by destroying science as a career. They could reverse this situation by matching the number trained to the demand, but they refuse to do so, or even to discuss the problem seriously (for many years the NSF propagated a dishonest prediction of a coming shortage of scientists, and most funding agencies still act as if this were true). The result is that the best young people, who should go into science, sensibly refuse to do so, and the graduate schools are filled with weak American students and with foreigners lured by the American student visa."Paul Cookhttps://plus.google.com/110983481653378694769noreply@blogger.com18tag:blogger.com,1999:blog-8759090.post-1150402455487055882006-06-15T19:58:00.000+00:002006-06-15T20:14:15.553+00:00The Klein Four (A group)Perhaps <a href="http://en.wikipedia.org/wiki/The_Klein_Four">The Klein Four</a> have passed you by as well as me. Well fret not. They are an a capella group from the maths department of Northwestern Univeristy and they shot to fame last year with their love song <span style="font-style:italic;">Finite Simple Group of Order Two</span>, which can be watched online:<br /><br /><object width="425" height="350"><param name="movie" value="http://www.youtube.com/v/UTby_e4-Rhg"></param><embed src="http://www.youtube.com/v/UTby_e4-Rhg" type="application/x-shockwave-flash" width="425" height="350"></embed></object><br /><br />They have an album out, full of more maths puns than you can shake a <strike>stick</strike> log at, which you can purchase via their <a href="http://www.kleinfour.com/">website</a> (where you can see some of their other performances) or even via <a href="http://phobos.apple.com/WebObjects/MZStore.woa/wa/viewAlbum?id=128602211&s=143444">iTunes</a>. <br /><br />The <a href="http://en.wikipedia.org/wiki/Klein_four-group">Klein four group</a>, or Vierergruppe, is a direct product of two copies of Z_2, and allows us to solve the quartic.Paul Cookhttps://plus.google.com/110983481653378694769noreply@blogger.com6tag:blogger.com,1999:blog-8759090.post-1150372414680793962006-06-15T11:53:00.000+00:002006-06-15T11:55:32.653+00:00When Art is Not ArtVia the BBC, <a href="http://news.bbc.co.uk/1/hi/england/southern_counties/5081744.stm">Empty plinth sidelines sculpture</a> a very funny, non-physics story about a sculptor who packaged his work together with a plinth for it to stand upon in a gallery. The Royal Academy of Arts decided that they had received two separate entries into the competition to be exhibited and a panel of judges decided that the plinth was the better work of art and put it on display. Hilarious.Paul Cookhttps://plus.google.com/110983481653378694769noreply@blogger.com2tag:blogger.com,1999:blog-8759090.post-1149687384728806362006-06-07T13:17:00.001+00:002011-01-26T18:32:48.082+00:00Cargese: The LecturesWell despite the beach life Cargese was a school and there were plenty of interesting lectures. The format for an average day was <blockquote>0800-0900hrs Breakfast<br />0900-1030hrs Lecture 1<br />1030-1100hrs Coffee break<br />1100-1230hrs Lecture 2<br />1245-1630hrs Lunch and beach break<br />1630-1730hrs Lecture 3<br />1800-1900hrs Lecture 4</blockquote> Which was very good and not too tiring. Most lecturers were given one morning and one afternoon slot, and frequently this wasn't enough time to bridge the gap between being completely pedagogical and also interesting to the experts in the audience. Let me give a list for posterity of all the talks we heard. Suggeseted preparatory literature for the talks can be found <a href="http://www.lpthe.jussieu.fr/cargese/schedule.shtml">here</a>.<br /><br /><span style="font-weight: bold;">BPS Black Holes by Bernard de Wit</span><br /><span style="font-weight: bold;">Black Holes, Attractors and Topological Strings by Andrew Strominger</span><br /><span style="font-weight: bold;">The Standard Model in String Theory from D-branes by A. Uranga</span><br /><span style="font-weight: bold;">Time dependence and space-like singularities in String theory by M. Berkooz</span><br /><span style="font-weight: bold;">Strings, Cosmology and Supersymmetry Breaking by S. Kachru</span><br /><span style="font-weight: bold;">Multitrace deformations of vector and adjoint theories and their holographic duals by Rabinovici</span>Paul Cookhttps://plus.google.com/110983481653378694769noreply@blogger.com1tag:blogger.com,1999:blog-8759090.post-1148837873242477352006-05-28T17:34:00.000+00:002006-06-05T13:32:37.480+00:00Living in the Theorists' ParadiseI find myself surrounded by the very pleasant <a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://photos1.blogger.com/blogger/1292/610/1600/Picture%28327%29.jpg"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;" src="http://photos1.blogger.com/blogger/1292/610/200/Picture%28327%29.jpg" border="0" alt="" /></a>scenery of Corsica, where I am attending the <a href="http://www.lpthe.jussieu.fr/cargese/">Cargese Summer School</a>. I am sitting in a computer room, opposite the lecture theatre and there is a gentle mineral fragrance in the air carried by the rain. Fortunately this is the last day of the school and the first day an afternoon trip to the beach has been rained off. That's right: trips to the beach, and theoretical physics. Sometimes it is good to stop and appreciate your fortune. <br /><br />The Cargese school commenced two weeks ago and covered a number of topics under the heading 'Strings and Branes: The present paradigm for gauge interactions and cosmology'. The school is located 20 minutes from the village of Cargese and is situated on the beach: at least it's a 2 minute walk to the beach from the institute, and views from the rooms on-site overlook a wonderful seascape, cliffs, beach and all. But, I gush... suffice it to say, it really is very nice here, and it is a pleasure to be here.<br /><br />Not only is it nice it is steeped in physics history. For example, there is a peninsula called the t'Hooft peninsula where <a href="http://en.wikipedia.org/wiki/Gerard_%27t_Hooft">t'Hooft</a> is supposed to have sat down and worked through the ideas that led to his Nobel prize on gauge theories and renormalization. I sat on the same peninsula, but I had forgotten my sunblock and had to retreat prior to having any great thoughts. In the garden of the institute is a tree, which is referred to as the wisdom tree, where students gather for discussion (in theory) and where it is said the lecturers have, in the past, climbed up into the branches of the tree to regail the students. Who can say how much truth there is in this. There was, in fact, some confusion as to which tree was indeed the one, true Wisdom Tree. All very worthy of Enid Blyton rather than the high energy physics community. From the garden it is possible to look out past the trees and locate a small island about a mile or so out in the sea. This is referred to as Polyakov Island after <a href="http://en.wikipedia.org/wiki/Alexander_Polyakov">Polyakov</a> swam out to it during one school. So, there is a sense of taking part in the continuation of physics lore while you are here. Perhaps the most astonishing feature of the school is it's two dogs: Calabi-Yau and Instanton. Calabi-Yau<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://photos1.blogger.com/blogger/1292/610/1600/Picture%28324%29.jpg"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;" src="http://photos1.blogger.com/blogger/1292/610/200/Picture%28324%29.jpg" border="0" alt="" /></a> is seemingly quite an old dog, and saunters in and out of lectures at will (his world-weary presence, often asleep at the front is deemed a measure of respect for the lecturer, after all Calabi-Yau has probably listened to many more lectures in Cargese than anyone present - he probably already knows the full quantum theory of gravity and may be the most well-educated dog in the world). Furthermore on the nights spent in town he would invariably make the twenty minute journey and come and find us, even is we were stationed at house in town for a party, (where he would wait of his own volition patiently outside for our departure) and then he would join us for the journey home along the dark road. Although it is in truth hard to say who was leading whom. Not only is he probably the smartest dog in the world (if Carlsberg made dogs...) but he's also a wild party animal too. See picture above of Calabi-Yau working at full capacity.<br /><br />I want to give you a feeling for some of the practical details of getting to Cargese just in case you are thinking of attending in the future. First off: the high energy physics school occurs every two years - if it's a World Cup or European Cup year then the school is on too and you have to apply early in the year. Registration this year closed in February. Cargese is on the south-west coast of Corsica, about an hours ride from Ajaccio airport, and you will almost certainly have to change flights somewhere in France to find a plane that will land in Ajaccio. The island has been invaded a number of times and this is reflected by the fact that you can get by speaking Italian here instead of French if you wish. Of course the modern invader is the tourist and so you can also survive using English, with a smattering of French. In fact, the locals do not like the people who buy a home here just for the holiday season and such houses have been known to burn down. Since you are likely to be taking a connecting flight you might want to be wary of one flight being delayed. This had significant financial implications for me since there were only two buses available from Ajaccio to Cargese upon arrival, and when my flight was delayed (resulting in 5 hours sitting in a Parisian cafe at the terminal in Orly, Paris - not quite 'living the dream') we had to hire a taxi at a cost of 130euros - this was subsidised by the School, and reduced to 100euros. You might think that arriving after midnight with no-one to meet you might be a problem but life at the Institute is very relaxed - so there was a poster on the wall and written in green ink was my name alongside the others who were late arrivals. Next to my name was a room number where I would be sleeping. The room was left open and keys were inside. The Institute is significantly remote for this calm attutude to security to be viable. But it is the little things like this that help to make Cargese a very peaceful place to be. The only other practical advice I can give you is that, just as in The Hitchhiker's Guide to the Galaxy, you should bring a towel. <br /><br />The peaceful setting of the school and the emphasis of a healthy mixture of relaxation and work are wonderful. The mixture of mostly PhD students and young Postdocs was great for initiating collaborations and building relationships for future work and the school itself is the best I have been to during my PhD. Not only in terms of meeting fellow students but also in terms of the lecture quality. We heard lectures from De Wit, Strominger, Harvey, Douglas and Connes amongst others, and we even got to feel "the power of Nekrasov", on topics ranging from black hole entropy to noncommutative geometry with a healthy dose of lectures about realising the standard model in the string theory picture. <br /><br />In the days of the cold war the school was funded by Nato and operated as a forum for bringing non-soviet scientists together. These days the event is quite global, but without a cold war the funding harder to come by. The school this year was supported by the European Science Foundation and CERN and a hearty thank-you is offered to the organisers of the school for the marvellous job they did to make this happen. So thank-you's to: <a href="http://string.lpthe.jussieu.fr/lpthe/members.pl?key=3">Laurent Baulieu</a>, <a href="http://www.phys.huji.ac.il/~eliezer/">Eliezer Rabinovici</a>, <a href="http://staff.science.uva.nl/~jdeboer/">Jan de Boer</a>, <a href="http://www.physics.rutgers.edu/people/pips/Douglas.html">Michael Douglas</a>, <a href="http://www-spht.cea.fr/pisp/vanhove/home_eng.html">Pierre Vanhove</a> and <a href="http://string.lpthe.jussieu.fr/members.pl?key=18">Paul Windey</a>. Without their organisation of funding, speakers, participants, schedule, support and ringing of the cowbell (although none had quite the enthusiastic glint in their eye as Pierre Vanhove when he got his hands on the bell) to get us into the lectures, Cargese quite simply would not have occurred, and it is hard to imagine it being organised any more successfully than this group managed. A special thank-you must also be reserved for Elena who took charge of all the school's administration and ensured everything ticked over nicely during the two weeks.<br /><br />Some pictures and commentary on the lectures to follow. <br /><br />I hate to trip but I gotta 'lope.Paul Cookhttps://plus.google.com/110983481653378694769noreply@blogger.com9tag:blogger.com,1999:blog-8759090.post-1148262685706574422006-05-22T00:32:00.000+00:002006-05-22T01:51:25.756+00:00Back in BlackWell it's been a while... I've often heard people wonder how researchers find the time to write a blog and do their work. Well while some bloggers are superhuman, this one is not. I've had a busy and not to mention stressful start to the year and really the blog only gets my attention when everything else is in good working order. What have I been up to? Well first of all I was applying for postdoc positions earlier in the year, the necessary finger-crossing meant that typing a blog became impossible for a short while. <a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://photos1.blogger.com/blogger/1292/610/1600/Lightmatter_pisa.jpg"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;" src="http://photos1.blogger.com/blogger/1292/610/200/Lightmatter_pisa.jpg" border="0" alt="" /></a>I was offered and accepted very happily a position at the <a href="http://www.sns.it/en/">Scuola Normale Superiore di Pisa</a> where <a href="http://www.sns.it/en/scienze/menunews/docentiscienze/sagnotti/">Augusto Sagnotti</a> has recently moved. Much hurrahing all round. Second I have just been working hard on what will be the last part of my thesis. That's not to say the thesis is all written up and ready to submit, oh no I have left two months for that, and a spare third, just in case. Finally, a confession: I really haven't been to any seminars for ages now. It's peculiar but the seminar series at KCL has dried up for the last few weeks. So today I tidied up my papers, organised my room and put everything in its right place to begin writing up. But of course I better get my blog up to date first so I can give a running commentary of sorts on the ups and downs of submitting a thesis.<br /><br />In my absence there have been a number of exciting papers on E10 and E11, in particular:<blockquote><li><a href="http://www.arxiv.org/abs/hep-th/0603255">Enhanced Coset Symmetries and Higher Derivative Corrections</a> by Neil Lambert and Peter West</li><li><a href="http://www.arxiv.org/abs/hep-th/0604143">Curvature corrections and Kac-Moody compatibility conditions</a> by Thibault Damour, Amihay Hanany, Marc Henneaux, Axel Kleinschmidt and Hermann Nicolai</li><li><a href="http://www.arxiv.org/abs/hep-th/0604143">IIA and IIB spinors from K(E10)</a> by Axel Kleinschmidt and Hermann Nicolai</li></blockquote>The first two demonstrate the very exciting emergence of higher derivative terms very naturally from the large algebra approaches, in the first case for E11 and in the second case for E10. The third paper continues the success of the E10 research teams ability to find fermions in their approach, for which there is as yet no equivalent result for E11.<br /><br />There have also been numerous great links from the other blogs, via <a href="http://motls.blogspot.com/">Lubos</a> we have <a href="http://video.google.com/videoplay?docid=6586235597476141009&q=feynman&pl=true">the Horizon episode on Feynman</a>, from which the stories will be very familiar, but it might be nice to see the man himself telling them. Thanks to <a href="http://www.math.columbia.edu/~woit/wordpress/">Peter Woit</a> we have links to all <a href="http://www.damtp.cam.ac.uk/estg06/table2.html">the talks</a> at the recent <a href="http://www.damtp.cam.ac.uk/estg06/eurostrings.htm">Eurostings 2006</a> conference in Cambridge. Of particular interest to those predisposed to very large algebras are,<blockquote><li><a href="http://www.damtp.cam.ac.uk/estg06/talks/west/index.html">E11 and Ten Forms</a> by Peter West</li><li><a href="http://www.damtp.cam.ac.uk/estg06/talks/kleinschmidt/index.html">Hidden Symmetries and Fermions in M-Theory</a> by Axel Kleinschmidt</li></blockquote>Since videos and transparancies are available for all talks this conference site is highly recommended, also of interest will be the following talks:<blockquote><li><a href="http://www.damtp.cam.ac.uk/estg06/talks/mathur/index.html">The Quantum Structure of Black Holes</a> by Samir Mathur</li><li><a href="http://www.damtp.cam.ac.uk/estg06/talks/silverstein/index.html">Singularities, Black Holes, and Attractor Explosions</a> by Eva Silverstein</li></blockquote>But there are plenty of good talks available here, so go and find out the latest from your favourite stringy research area.<br /><br />Also I've noticed two review articles for the E11 approach to M-Theory are now available on the archive. They are both a couple of years old, but worth a look:<blockquote><li><a href="http://www.arxiv.org/abs/hep-th/0604145">Algebraic structures in M-theory</a> by Ling Bao<br /></li><li><a href="http://www.arxiv.org/abs/hep-th/0404235">Hidden Symmetry Unmasked: Matrix Theory and E(11)</a> by Shyamoli Chaudhuri</li></blockquote>Now I have to make sure my thesis is nothing like these reviews...Ho-hum. <br /><br />So let's see, things to do: 1. Learn Italian 2. Write-up thesis. So... the first thing I am going to do is fly off to Corsica tomorrow for the <a href="http://string.lpthe.jussieu.fr/cargese/">Cargese summer school</a> (at much personal sacrifice to my better desires to start writing up!), and internet permitting I'll try and write some blog postcards from there.<br /><br />I've just checked the weather and tomorrow it's supposed to be 31 Celcius and sunny, which sure beats the grey sheets of rain we had in Greenwich today.Paul Cookhttps://plus.google.com/110983481653378694769noreply@blogger.com7tag:blogger.com,1999:blog-8759090.post-1143122504107373102006-03-27T17:34:00.000+00:002006-03-27T15:52:16.883+00:00Kallosh on AttractorsYesterday we heard the first of three different talks from <a href="http://www.stanford.edu/dept/physics/people/faculty/kallosh_renata.html">Renata Kallosh</a>. Her first chosen specialist subject was innocuously titled <span style="font-style:italic;">BPS and non-BPS Black Hole Attractors</span>. This first talk really was for the back row of the audience at our school, where all the experts were sitting. <a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://photos1.blogger.com/blogger/1292/610/1600/kallosh.jpg"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;" src="http://photos1.blogger.com/blogger/1292/610/200/kallosh.jpg" border="0" alt="" /></a>Perhaps due to the time constraint, quantities were not defined and many ideas were assumed to be known by the audience. Unfortunately there is much work for me to do. At one point she paused and said to the audience: <blockquote>"So far I was a bit sketchy...but this is something you can read. This is a known result."</blockquote> Well this is true enough, so here are the references for Kallosh's first talk (just 1 hour):<br /><blockquote><li><a href="http://www.arxiv.org/abs/hep-th/9702103">Black holes and critical points in moduli space by S. Ferrara, G. W. Gibbons and R. Kallosh</a></li><li><a href="http://www.arxiv.org/abs/hep-th/0511117">Non-Supersymmetric Attractors in String Theory by P.K. Tripathy and S. P. Trivedi</a></li><li><a href="http://www.arxiv.org/abs/hep-th/0602005">The non-BPS black hole attractor equation by R. Kallosh, N. Sivanandam and M. Soroush</a></li><li><a href="http://www.arxiv.org/abs/hep-th/9509160">The Symplectic Structure of N=2 Supergravity and its central extension by A. Ceresole, R. D'Auria and S. Ferrera</a></li><li><a href="http://arxiv.org/abs/hep-th/9602014">E(7) Symmetric Area of the Black Hole Horizon by Renata Kallosh, Barak Kol</a></li><li><a href="http://arxiv.org/abs/hep-th/9608059">STU Black Holes and String Triality by Klaus Behrndt, Renata Kallosh, Joachim Rahmfeld, Marina Shmakova, Wing Kai Wong</a></li><li><a href="http://arxiv.org/abs/hep-th/9612076">Calabi-Yau Black Holes by Marina Shmakova</a></li></blockquote>It would have been good to know these papers well before the talk began and as you can imagine the school degenerated to a workshop for the experts during this talk. However there were plenty of interesting things for us beginners to pick up. Such as that N=2 special geometry is useful and that symplectic invariants are useful. I'll try and reproduce my beginner's conception of special geometry in this post, mostly with the help of Christiann Hofman's masters' thesis, <a href="http://www.weizmann.ac.il/home/hofman/publication.html">Dualities in N=2 String Theory</a> (you can find the link near the bottom of the page).<br /><br />Special geometry is the name given for the geometry associated to the scalar couplings of the vector and hypermultiplets of theories involving 8 supercharges, although the original use of the name was restricted to N=2, vector multiplets and four dimensions. Recall that the vector multiplet is an irreducible multiplet of super <a href="http://en.wikipedia.org/wiki/Yang-Mills">Yang-Mills theory</a>, it is the enhancement of the gauge field to the supersymmetric setting, and has field content:<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://photos1.blogger.com/blogger/1292/610/1600/vector.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;" src="http://photos1.blogger.com/blogger/1292/610/320/vector.jpg" border="0" alt="" /></a> Where X is a complex scalar, omega is a pair of spinors, Y is a triplet of scalars (arranged in an anitsymmetric 2 by 2 matrix) and A is a real gauge boson. For reference the hypermultiplet, when there are no central charges contains the fields:<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://photos1.blogger.com/blogger/1292/610/1600/hyper.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;" src="http://photos1.blogger.com/blogger/1292/610/320/hyper.jpg" border="0" alt="" /></a> Here, A is a pair of scalar doublets, and zeta is a pair of spinors. When we include gravity in our supersymmetric gauge theory setting we find the metric is enhanced to the gravity multiplet, or Weyl multiplet, consisting of the metric and two fermionic fields of spin 3/2 called gravitini. These gravitational fields can couple to the content of the vector and hyper multiplets. Furthermore an additional vector multiplet is required if we wish to break auxillary gauge symmetries (see <a href="http://www-lib.kek.jp/cgi-bin/kiss_prepri?KN=198501299&OF=4.">Lagrangians of N=2 supergravity-matter systems by de Wit, Lauwers and Van Proeyen</a>). Only the vectors have physical significance, the remainder of the multiplets are auxillary fields. So if we commence with n vector multiplets from our super Yang-Mills theory, and then we include gravity to construct a sensible local theory, we find we require n+1 gauge fields. These gauge fields are the equivalents of our familiar Maxwell gauge field in electromagnetism, and including the dual fields we have 2(n+1) fields which are transformed into each other by the action of the symplectic group Sp(2n+2,R). The flux integrals of the field strengths and their duals give us electric, q, and magnetic, p, charges, and the symplectic transformation is interpreted as the generalization of electric-magnetic duality. So far, so good. But we neglected to mention that we also have n scalar fields which do not transform in such a well-mannered way under the symplectic group action. A suitable projective coordinate reparameterisation (giving us n+1 scalars) will, however, do the job, see Mohaupt's review <a href="http://www.arxiv.org/abs/hep-th/0512048">Strings, higher curvature corrections and black holes</a> for the overview. The scalars of the Lagrangian may be thought of as coordinates and, under the restrictions of supersymmetry, the geometry of the complex symplectic vector space C(2n+2)associated to the scalar coordinates is called special geometry. We end up with coordinates on our manifold, coming from the prepotential and the projective coordinate which do transform as a symplectic vector. However symplectic geometry is a little different from Riemannian geometry, for example <a href="http://en.wikipedia.org/wiki/Symplectic_geometry">symplectic manifolds</a> have no local invariants like curvature.<br /><br />If, like me, you have never come across any of this technology before you can see that there is plenty of work to do. Especially in picking up terminology and generic constructions. But don't despair! Take heart, all the experts at the school in Frascati presented some very pretty results (I was able to understand this from the joy in their eyes - inc omcing to this conclusion I have assumed the sanity of the speakers...) and it would seem the end result is worth the work.Paul Cookhttps://plus.google.com/110983481653378694769noreply@blogger.com4tag:blogger.com,1999:blog-8759090.post-1143047199392343282006-03-22T16:49:00.001+00:002011-01-26T18:33:28.802+00:00AttractorsLast Monday and Tuesday saw the start of the Winter school on Supersymmetric Attractor Mechanism here in Frascati. I have already described a little of the content of Per Kraus' talks, but we also have had a series of talks by his frequent collaborator <a href="http://www-personal.umich.edu/%7Elarsenf/personal/personal.html">Finn Larsen</a>. Larsen has given three talks under the title <span style="font-style: italic;">Introduction to Attractors with applications to Black Rings</span> and based upon his paper with Kraus: <a href="http://www.arxiv.org/abs/hep-th/0503219"><span style="font-style: italic;">Attractors and Black Rings</span></a>. At some point there will be a video online. At least one was made, and it seems there is a certain attractor mechanism for all real world content to eventually stabalise on the internet, so it seems fair to expect it will appear one day. I'll let you know if I hear anything.Paul Cookhttps://plus.google.com/110983481653378694769noreply@blogger.com0tag:blogger.com,1999:blog-8759090.post-1142845635926291312006-03-22T15:00:00.000+00:002006-03-22T14:03:27.506+00:00If on a Winter's Night a Physicist...So, I find myself in Frascati, just 20km south-east of Rome attending <a href="http://www.lnf.infn.it/~bellucci/SAM2006.html">SAM 2006</a> (School on the Attractor Mechanism). This is my first visit to Italy, and so very exciting for me (food, coffee, wine, olives, historic sites, art, physics...). There are 30 or so of us here at the Instituto Nazionale di Fisica Nucleare, where all the roads are named after famous theoretical physicists! The high energy bulding is on <a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://photos1.blogger.com/blogger/1292/610/1600/Picture%28249%29_2.jpg"><img style="float:left; margin:0 10px 10px 0;cursor:pointer; cursor:hand;" src="http://photos1.blogger.com/blogger/1292/610/320/Picture%28249%29_2.jpg" border="0" alt="" /></a>Via P. Dirac, which at some point turns into Via R. Feynman, a nice continuity. There are also roads for Pauli, Heisenberg, Schrodinger, Planck and others, but no Via Einstein! Of course the institute itself lies on the main road named after Enrico Fermi, so he doesn't appear on the campus map either, but that's okay. <br /><br />The school was billed for beginners, and that is why I am here. Yesterday and today, we heard from <a href="http://personnel.physics.ucla.edu/directory/faculty/index.php?f_name=kraus">Per Kraus</a> and <a href="http://www-personal.umich.edu/~larsenf/personal/personal.html">Finn Larsen</a>. Kraus talked under the title <span style="font-style:italic;">"Black Hole Entropy and the AdS/CFT Correspondence"</span> and I hope there will eventually be a video of the talk available online, but we shall see... For the impatient you can already<a href="http://arxiv.org/abs/hep-th/0508218">watch/listen to Kraus giving a talk</a> based around his papers <span style="font-style:italic;"><a href="http://arxiv.org/abs/hep-th/0506176">Microscopic Black Hole Entropy in Theories with Higher Derivatives</a></span> and <span style="font-style:italic;"><a href="http://arxiv.org/abs/hep-th/0508218">Holographic Gravitational Anomalies</a></span> both with Fin Larsen. But I think the video of the three hour talk from our school will be much more elementary and welcoming. Hopefully I can make some comments about Fin Larsen's complementary talks in a later post.<br /><br />Kraus began by telling us about the <a href="http://www.arxiv.org/abs/%5Bhep-th/9204099">BTZ black hole</a> (so-called for Banados, Teitelboim and Zanelli), emphasising the point that only for the BTZ black hole does a precise agreement occur between the microscopic and macroscopic counts of black hole entropy . The BTZ black hole is a 3-dimensional black hole similar to the Kerr solution, for a review see Carlip's <span style="font-style:italic;"><a href="http://arxiv.org/abs/gr-qc/9506079">The (2+1)-Dimensional Black Hole</a></span>. It lives in three dimensional <a href="http://en.wikipedia.org/wiki/Anti_de_Sitter_space">anti de Sitter space</a>, AdS_3, a space with negative cosmological constant. Identifications in AdS_3 give rise to the BTZ black hole. <br /><br />AdS_3 can be realised as a hyperboloid in a signature (+,+,-,-), i.e.<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://photos1.blogger.com/blogger/1292/610/1600/AdS.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;" src="http://photos1.blogger.com/blogger/1292/610/320/AdS.jpg" border="0" alt="" /></a>. This is the Sl(2,R) group manifold. The BTZ black hole can be analysed by looking at the conjugacy classes of Sl(2,R). There are three conjugacy classes: hyperbolic, elliptic and parabolic, with the BTZ black hole sitting in the hyperbolic conjugacy class. Kraus, Samuli Hemming and Esko Keski-Vakkuri have written about this in <span style="font-style:italic;"><a href="http://arxiv.org/abs/hep-th/0208003">Strings in the Extended BTZ Spacetime</a></span>, see section 2. An identification is made with the conjugating elements and the left and right moving temperature, and we move into a thermodynamic setting. Mass, angular momentum, entropy formulae follow, and the equivalence of a thermal AdS_3 background with a BTZ upto various modular transformations in each case.<br /><br />Kraus considered spacetimes whose near horizon geometry (when r approaches the event horizon, and considering only the dominant terms) factorises into AdS_3 x X x S^p, where X is an unspecified geometry (see Strominger's <span style="font-style:italic;"><a href="http://www.arxiv.org/abs/hep-th/9712251">Black Hole Entropy from Near-Horizon Microstates</a></span> for the motivation for looking at this geometry). Kraus demonstrated the equivalence of the <a href="http://www.arxiv.org/abs/gr-qc/9307038">Wald formula</a>, for finding the entropy from a Lagrangian which includes higher-derivative corrections, with the Cardy density of states formula for a CFT for theories which have a general diffeomorphism invariance. Through this equivalence the exact entropy (i.e. including corrections) is derived solely from knowing the central charges of the theory. Furthermore Kraus presented a variational principle to give the central charge for some Lagrangian with higher derivative terms. In his final talk he looked at the use of gravitational anomalies for learning about the pictures on either side of AdS/CFT.<br /><br />Kraus used two main examples to illustrate his talk:<blockquote><li>D1-D5-P on T^4 x S^1 or K3 x S^1</li><li>M5 branes wrapped on 4-cycles in M-theory on CY_3 x S^1</li></blockquote> He demonstrated how the BTZ black hole appears in each case and compared the entropy calculations in each case. The D1-D5-P entropy (<a href="http://arxiv.org/abs/hep-th/9601029">Strominger and Vafa</a>) is in exact agreement with the macroscopic Bekenstein-Hawking entropy, while the M5 branes' microscopic entropy (<a href="http://arxiv.org/abs/hep-th/9711053">Maldacena, Strominger and Witten</a>) gives a central charge consisting of two parts, the highest order part agreeing with the macroscopic count and the remainder being due to the presence of higher derivative terms in M-theory. I refer you to the two papers with Larsen linked to earlier to see the full application of the method with these examples in mind.Paul Cookhttps://plus.google.com/110983481653378694769noreply@blogger.com6tag:blogger.com,1999:blog-8759090.post-1141260484886750312006-03-01T23:28:00.000+00:002006-03-08T11:32:34.700+00:00Classifying Rational Conformal Field Theories<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://photos1.blogger.com/blogger/1292/610/1600/Terry%20Gannon.jpg"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;" src="http://photos1.blogger.com/blogger/1292/610/200/Terry%20Gannon.jpg" border="0" alt="" /></a>Yesterday afternoon was quite a chilly day in London, the kind of day when being crammed into a packed and warm lecture room below ground level in the basement of Queen Mary college from where you can hear the tube rattle by was quite an attractive prospect. So at three in the afternoon yesterday that's where I and other London theoretical physicists gathered to hear <a href="http://www.math.ualberta.ca/~tgannon/">Terry Gannon</a> talk about "The classification of RCFTs". <br /><br />First off, it gives me great pleasure to report to you that the "damn book" is finished :) after five years of hard slog Terry's book, <span style="font-style:italic;"><a href="http://www.amazon.co.uk/exec/obidos/ASIN/0521835313/qid=1141256104/sr=8-1/ref=sr_8_xs_ap_i1_xgl/203-0952502-3222356">Moonshine Beyond the Monster</a></span> and available to buy from the 31st August, 2006. Hurrah. There's an excellent documentary by Ken Burns on the <a href="http://www.imdb.com/title/tt0098769/">American Civil War</a> that took longer to make than the war itself, I have no doubt that it will take me inestimably longer to understand this 538 page book than it took to write. Fortunately noone died in the making of the book, to the best of my knowledge. For some history of the Monster see Terry's <span style="font-style:italic;"><a href="http://arxiv.org/abs/math.QA/0402345">Monstrous Moonshine: The First Twenty-Five Years</a></span>.<br /><br />Terry described his approach to trying to classify Rational Conformal Field Theories (you could look at <a href="http://en.wikipedia.org/wiki/Rational_conformal_field_theory">Wikipedia for a brief definition of a RCFT</a>, or a much better idea might be to start learning about CFT from scratch with Paul Ginsparg's Les Houches lectures, <span style="font-style:italic;"><a href="http://arxiv.org/abs/hep-th/9108028">Applied Conformal Field Theories</a></span> or Krzysztof Gawedzki's <span style="font-style:italic;"><a href="http://www.cgtp.duke.edu/QFT/fall/index.html">Lectures on Conformal Field Theory</a></span>) by searching for invariants of the chiral algebra, or Frobenius algebra, that underlies the RCFT. By way of comparison, Terry said that the very succesful classification of the Lie algebras rested upon the invariant of the Dynkin diagram. But what invariants are worth considering, whose discovery will tell us most of the information about the algebra? Terry suggested two:<blockquote><li>modular invariants (i.e. partition function on the torus)</li><li>NIM representations (i.e. partition function on the cylinder)</l></blockquote> But he only had enough time to talk a little about the first and describe to us the modular functions that appear. <br /><br />To commence one must settle upon a chiral algebra, or a vertex operator algebra, and Terry told us that some very nice choices are the affine Kac-Moody algebras (see Fuchs' <span style="font-style:italic;"><a href="http://arxiv.org/abs/hep-th/9702194">Lectures on conformal field theory and Kac-Moody algebras</a></span> section 16 for the definitions). A level, k, must also be picked. We were told that one way to imagine a chiral algebra is as a complexification, or 2-dimensionalisation, of a Lie algebra. If we denote all the objects appearing in a Lie algebra by a tree diagram, having all the properties of the Lie bracket at the branch (i.e. antisymmetric...) then the complexified version of the algebra turns each of the branches of the tree diagram into a cylinder:<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://photos1.blogger.com/blogger/1292/610/1600/loopalgebra.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;" src="http://photos1.blogger.com/blogger/1292/610/320/loopalgebra.jpg" border="0" alt="" /></a> For more about this way of complexifying to get loop algebras we were referred to the work of <a href="http://www.rci.rutgers.edu/~yzhuang/">Yi-Zhi Huang</a>, in particular his book <span style="font-style:italic;"><a href="http://www.fetchbook.info/fwd_description/search_0817638296.html">Two-Dimensional Conformal Geometry and Vertex Operator Algebras</a></span>.<br /><br />Returning to the CFT, the Hilbert space is described by irreducible representations of our affine algebra (left moving and right moving copies) which for a given level k, are paramaterised by highest weight labels. For the example of affine SU(2), the highest weights are characterised by two labels (<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://photos1.blogger.com/blogger/1292/610/1600/l0.jpg"><img style="cursor:pointer; cursor:hand;" src="http://photos1.blogger.com/blogger/1292/610/200/l0.jpg" border="0" alt="" /></a>, <a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://photos1.blogger.com/blogger/1292/610/1600/l1.jpg"><img style="cursor:pointer; cursor:hand;" src="http://photos1.blogger.com/blogger/1292/610/200/l1.jpg" border="0" alt="" /></a>) such that <a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://photos1.blogger.com/blogger/1292/610/1600/l0.jpg"><img style="cursor:pointer; cursor:hand;" src="http://photos1.blogger.com/blogger/1292/610/200/l0.jpg" border="0" alt="" /></a> + <a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://photos1.blogger.com/blogger/1292/610/1600/l1.jpg"><img style="cursor:pointer; cursor:hand;" src="http://photos1.blogger.com/blogger/1292/610/200/l1.jpg" border="0" alt="" /></a> = k. The Hilbert space may be written as:<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://photos1.blogger.com/blogger/1292/610/1600/hilbertspace.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;" src="http://photos1.blogger.com/blogger/1292/610/320/hilbertspace.jpg" border="0" alt="" /></a>Where M is the multiplicity, and the one-loop partition function for this RCFT may be written in terms of the characters, <a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://photos1.blogger.com/blogger/1292/610/1600/character.jpg"><img style="cursor:pointer; cursor:hand;" src="http://photos1.blogger.com/blogger/1292/610/200/character.jpg" border="0" alt="" /></a>:<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://photos1.blogger.com/blogger/1292/610/1600/partition.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;" src="http://photos1.blogger.com/blogger/1292/610/320/partition.jpg" border="0" alt="" /></a> It turns out that the characters are modular functions, and are subject to the familiar S and T transformations:<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://photos1.blogger.com/blogger/1292/610/1600/SandT.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;" src="http://photos1.blogger.com/blogger/1292/610/320/SandT.jpg" border="0" alt="" /></a> Furthermore, the partition function is modular invariant and characterised by its multiplicities, M.<br /><br />At this point in the talk, Terry had about six minutes remaining and had arrived at what he thought of as the start of his talk, and defined the "modular invariant" he hoped to use to classify RCFTs:<blockquote>Given some affine algebra at level k, a modular invariant is a matrix M of multiplicities describing the partition function, Z, such that, <a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://photos1.blogger.com/blogger/1292/610/1600/modularinvariant.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;" src="http://photos1.blogger.com/blogger/1292/610/200/modularinvariant.jpg" border="0" alt="" /></a></blockquote> Terry told us that these conditions gave rise to RCFTs that are "just barely" classifiable. <br /><br />Terry finally asked us why bother classifying? Or, in his words, "who cares?" His answer was that the classification leads to interesting results. What more could you want? He gave us the example from Cappelli-Itzykson-Zuber from 1986 of the classification of affine su(2), which is completely classified for the levels, k, 4/k, k/2 is odd, k=10,16,28, and he told us a story he heard twice; once from Zuber about a correspondence he had with Victor Kac, and a second time the same story from Kac - so, he said, it must be a true story. It went like this: After having written down some of the classifications of affine su(2) in 1986, Zuber wrote to Kac about the results, who replied and pointed out the classification for k=10, which he said contained some exceptional numbers - literally numbers he thought came from the exceptional group E_6. Zuber said he didn't understand Kac nor pay it much heed until someone else repeated it years later and he dug out the letter, headed to the library and confirmed that all the numbers appearing in the classification do indeed have an intimate and mysterious (to this day...) relation with the groups A, D, E, and the symmetries of their Dynkin diagrams. At this point Terry bemoaned the fact that God was manifestly not benevolent since he insisted on making 2 a prime number...Terry's discomfort with 2 didn't seem justifiable until later on when he mentioned that his wife is expecting twins (excuse me for this weak pun) so I just put two and two together... :) <br /><br />So the ADE-classification arises mysteriously from modular invariants, so that's why to classify RCFTs: because they might be interesting.Paul Cookhttps://plus.google.com/110983481653378694769noreply@blogger.com12tag:blogger.com,1999:blog-8759090.post-1140434795574539532006-02-20T11:26:00.000+00:002006-02-20T11:51:07.460+00:00Does your ball roll at normal speed?Flying in the face of recent efforts to redefine the scientist stereotype, described at <a href="http://cosmicvariance.com/2006/02/14/the-scientists-image/">cosmic variance</a>, <a href="http://entropybound.blogspot.com/2006/02/whos-scientist.html">entropy bound</a> and <a href="http://www.inkycircus.com/jargon/2006/02/kids_say_the_da.html">inkycircus*</a>, comes the latest rebuttle from no less than<a href="http://en.wikipedia.org/wiki/Jose_Mourinho">Jose Mourinho</a>, who manages to make his feelings known during an interview about Chelsea's pitch condition prior to their Champion's League fixture with Barcelona: <blockquote><a href="http://news.bbc.co.uk/sport1/hi/football/teams/c/chelsea/4731380.stm">'Sometimes you see beautiful people with no brains. Sometimes you have ugly people who are intelligent, like scientists,' he said.<br /><br />'Our pitch is a bit like that. From the top it's a disgrace but the ball rolls at normal speed.'</a></blockquote>*By the way this is a great science news blog that I only just cottoned onto, which I heartily recommended to you all, if you haven't been there already.Paul Cookhttps://plus.google.com/110983481653378694769noreply@blogger.com4