UK Annual Theory Meeting

The semester has ended, there are no weekly seminars to write about, I have had my yearly winter cold (but that was not interesting enough to say much about) and now Christmas has come and gone, but just before it began (I mean December 25th rather than the retail definition of mid-October) I started to write up the following...

For the last few days I have been getting up much earlier than normal, meeting many more friends, listening to more lectures and eating larger meals than normal. This is not some new life plan undertaken on my part but rather I have been to Durham to attend the annual Christmas UK theory meeting. The meeting takes place every year near Christmas and has a prestigous history of speakers. It is also a meeting that attempts to present an overview of the current state of the art in theory ranging from phenomenology and the construction of particle accelerators to string theory and tries to find a balance between them (which is very hard, and invariably different talks were appreciated to different degrees by disparate groups, save the final one).

I arrived at Grey College, where we were housed, at quarter-to-one on Monday, a feat which required a near superhuman effort to awaken at six-thirty that morning. It was my first benefit of daylight saving time, there was pristine blue sky and it was actually pleasurable to see the light reflected from all the unfamiliar angles of the buildings near my home. Despite the lack of sleep, the three hour train journey at a cost of £88.00(!) was very pleasant. However the rest of the afternoon was not so nice for me, since the talks were dedicated to experimental particle physics. While string theorists must not decouple from experiment, it is very easy for a PhD student in strings, who has specialised in group theory, differential geometry and gravitational physics to never have come into contact with much QCD or lattice simulations and certainly not at the level of the talks that first afternoon, alas. Of course the same is true within any large subject area, and from this blog you will know how often I have had trouble even following stringy seminars. From the number of sleepers in the various talks I feel there was a similar disappointment for some of the phenomenologists and others during some of the stringier talks. Ho-hum.

The first talk was "Results from the B factories" by Steve Playfer, where we heard about the latest data cuts and fittings comng out of the Belle and BaBar experiments. What are Belle and BaBar? Well they're the B meson factories and they look to see whether charge (particle-antiparticle) and parity (physical mirror) symmetries are violated in the decay of the B and the anti-B, or B-bar. Belle is located at KEK in Japan and BaBar is at the Stanford Linear Accelerator in California. The two experiments have confirmed (BaBar 2002) that the B-mesons do violate CP-symmetry. Steve is part of the BaBar team and his talk describing recent results, hinting at future results and improvements in error ranges displayed a healthy amount of competitive spirit with the Belle experiment.

The rest of the afternoon was filled with talks possessing a phenomenological nature, and again outside your humble blogger's limited range of semi-enlightenment. The roll-call reads: "Heavy Flavour Physics" by Matthias Neubert and "Lattice QCD and results from CLEO" by Paul MacKenzie. The evening was spent in the pub and then subsequently the "trendy" wine-bar Jimmy Allen's where all the cocktails had decidedly dismal names, but nevertheless a good time was had.

The tuesday began much earlier than most tuesdays, perhaps this was the effect of the drink the night before or perhaps it was due to the hour. The first talk, "Twistors and Perturbative Gravity" was given by Dave Dunbar from Swansea University and was of a similar format to many of the twistor talks I have seen this year in that there was a long review of the material for the skeptics in the audience who, like me, have so far shied away from twistors and MHV amplitudes. As ever the simplification of loop calculations coming from twistors seemed nothing short of miraculous, and, as ever, I have made a solemn pledge to myself to read Witten's twistor paper and work through some of the calculations myself.

The second talk was a report from the front line on the construction of the LHC at Cern given by Jos Engelen. We saw pictures of heavily-laden lorries shipping extraordinarily large structures back and forth, heard tales about the pitfalls of purchasing specially made detector crystals from a Russian manufacturer who "forgot to pay their electricity bills" and subsequently upped the price for the consignment, and we marvelled at the design ingenuity of the engineers having to form these perfectly symmetric detectors at such a large scale and underground too, in prticular Jos told us about one detector whose perfect circular cross-section was designed only to be achieved once the final segment was installed and its weight would bring about the perfect circle. We heard abut the 27km track (how perhaps only the rate of intallation of the 50m magnets needs to speed up), Altlas, CMS, LHCb and
Alice. In short all is well, Jos paraphrased this:

"We are going to do the first new physics in Summer 2007. This sentence does not define new physics, it defines Summer 2007."

Vijay Balasubramanian spoke about his approach to "Gravitational Thermodynamics" which was quite different to all other talks on this subject that I have ever heard, for example there was almost no mention of charge ensembles (at least not until the questions at the end, when it was asked how his work relates to the more usual stringy appraoch to degrees of freedom). Before he began there was an advertisement for a postdoc position and a faculty position at the University of Plymouth, details to be found here. He spoke with great enthusiasm and volume about horizons and Unruh radiation and very large states. In gravitational thermodynamics the information loss paradox is side-stepped if black holes do theoretically contain all the degrees of freedom of the states that fall into them and that information could theoretically re-emerge from the black-hole, eventually. Pure states remain pure. Vijay was addressing the question of just what is a pure state and what would it take to be able to probe it. His arguments can be found in his paper with Vishnu Jejjala and Joan Simon, "The Library of Babel". But the main argument is that while states do remain pure and information is not lost, "almost no probes are able to differentiate the microstates of a black-hole". To find out what almost means you'll have to read the paper (7 pages), and I heartily encourage you to read the short story that the paper borrows its name from by Borges.

In the afternoon we had a very nice, pedagogical talk from Hans Peter Nilles, who amongst other things explained to us in detail exactly what an orbifold is. His title was "Grand Unification in Strings" and he said was based on work found here, here and href="http://www.arxiv.org/abs/hep-th/0504117">here.

Finally we ended the day with a talk by Keith Ellis, provocatively entitled "Marching Orders for QCD" which he said could be found online here, so I left. That evening also found me making further investigations into beverages of Jimmy Allen's.

The final morning began with Herman Verlinde building bridges between string theory and experimental particle physics. His title was "Geometry and the Standard Model" and his proposition was to decouple the landscape. He described the landscape as 10^500 doors with locks on, and suggested that we should start with the only key we have: the standard model. His aim was to start with the minimally supersymmetric standard model, to use this to find a moduli space for the SuSy vacua and to use this to find a configuration space of Calabi-Yau manifold singularities. The devil is in the detail, and he led us on a path that took in fractional branes, quiver gauge theory, Del Pezzo surfaces and how to draw a Moose. During the question session the attempt to build bridges between theory and experiment was welcomed, but only after the rivalry between string theorists and those hoping for a more readily tangible explanation of high-energy physics had once again flared up. A member of the audience had been willing to bet against string theory being the correct unifying theory, and Hermann Verlinde had steadfastly opposed his negative opinions by saying he was willing to take such a bet. This is the first time, beyond the internet, where I have witnessed any kind of head-on confrontation about the nature of string theory. I expect it will not be the last.

The final talk of the meeting was of a much more gentle nature and was enjoyed by a broad spectrum of the audience, regardless of their predisposition towards string theory. It was entitled "How did Einstein get the Nobel Prize?" given by the very entertaining Cecilia Jarlskog. She gave us a colourful review of the life of Alfred Nobel and the early history of the Nobel prize and we got to see all the nominations in the years leading up to Einstein's prize, and even to see some of the photocopies of handwritten letters of recommendation for the prize. All of which was very nice, and made for a fitting end to the meeting and also, for me, to the year of physics celebrating the centenary of Albert's miraculous year.

Dilogarithms

Two noteworthy events occured at King's College last Friday. One of which involved "one-hundred drunk LSE students" rioting in the lower levels of our Strand campus and the other did not. The rioters flooded our building and caused havoc, some attempted to invade the maths classrooms no doubt eager to benefit from the wisdom of our faculty, and others began ripping ceiling tiles from the English department in an attempt to seemingly tear a building to bits whilst still inside it, causing £30,000 worth of damage. The second event of note last Friday was our mathematics department colloquium which was given by the impressive Don Zagier under the title "Dilogarithms and the Bloch group: from algebraic K-theory to modular forms to conformal field theory". The rioters caused our colloquium to start late, a fact that was noted by Professor Zagier when nearly out of time he suggested that perhaps he himself could riot in order to circumvent the need to vacate the lecture thatre at the prescribed time so he could get to the end of his talk.

Permit me to pass on some brief comments from the beginning of Zagier's talk about the dilogarithm with the caveat that most of this remains beyond my ken. Nevertheless the dilogarithm has been studied by some truly great mathematicians including Euler, Leibnitz, Abel, Lobachevsky, Borel, Ramanujan, and others so if only for historical interest it is nice to look at some of the properties of the dilogarithm in passing.

We are all on first name terms with the logarithm function (that's log to you and me):
But perhaps not so well known is it's relation the dilogarithm: There are plenty of others, which are specific values, s, of the polylogarithm, or Jonquiére's function, Zagier told us that there are only 8 closed forms for the dilogarithm, some of which include the golden ratio, The only irrationals on the left hand side are powers of the golden ratio. We might look for properties of the dilogarithm that are similar to those we know of the logarithm, for example we know that, Zagier told us that there was no simple equivalent of this for the dilogarithm, but that we did have a formula, named for Abel even though it had been discovered by others before him (Spence, 1809) and after him (Lobachevsky), Zagier told those of us taking notes in the audience to just write "junk" instead of the right-hand-side of the above, however, he stressed that the order of the left-hand-side terms was important. I think practitioners of this art tend to normalise their dilogarithm functions into the Rogers L-function, which gets rid of the junk. There are a number of useful identities for the dilogarithm two of which are,These lead to equivalent forms of the five-term equation via X ~ 1/X ~ 1-X ~ 1/(1-X) ~ 1-(1/X) ~ X/(X-1). Furthermore if you define a junk-removing functional equation: Then this equation has a modulo 5 symmetry,Try it and see!

Zagier went on to look at the Bloch-Wigner dilogarithm, whose five-term equation is equal to zero and to give an argument in terms of the volume of tetrahedra in a hyperbolic 3-space modulo PSL_2(C) about why it should be zero. It sounded very nice, but I can't say I understood. For those interested the argument is given in section four of sixth set of notes by Matilde Lalin from classes given by Fernando Rodriguez Villegas called "Topics in K-Theory and L-functions". Those interested in seeing many more five-term functional equations should look through Kirillov's Dilogarithm Identities. For an introduction to dilogarithms Maximon's article seems a good place to commence.

Zagier talked fluently, rapidly and energetically about many more topics, such as the Bloch group (if you google Bloch group you may not find much helpful information but you will come across Dr. Bloch's group page), the five-term equation related to the Schrodinger equation for a cubic potential, K-theory (in particular K_3) and also rational conformal field theory, where he spoke with great enthusiasm of the recent conjectures of Werner Nahm. He never once, to my knowledge, resorted to rioting to extend his talk.

Beyond Einstein

Here's some very short (actually it's already started) notice of the physics equivalent of Live 8. To celebrate the world year of physics physicists, internet pioneers and others will be participating in a marathon 12-hour broadcast performing covers of classic pop songs to raise awareness of physics live on the web and will discuss Einstein's theory of special relativity and more. In the words of the BBC article,

Alongside E=mc², there will be discussion of gravitational waves, the search for the Higgs Boson and the mysteries that still linger behind Einstein's work.

So get the popcorn in, get broadband installed and go and watch (or put on in the background) the webcast at Beyond Einstein. Just so you know there are some well known names who will be participating later on today. Included, amongst others, on the list is (broadcast times are in brackets and are Central European Times):

Albert Einstein (1200-0000)

David Gross(1700)

Gerard't Hooft (1700)

Murray Gell-Mann(1700)

Paul Davies (2230)

Stephen Hawking (TBC)

Quite a list eh? Although there must be some code for the yellow and green stripes on the particpator list I presume they are all taking part. The full programme is available here.

Given that this is obviously a very-well prepared event it is amazing not to know anything about it until after it has begun! Clifford at cosmicvariance also found about it today, and I only heard about it thanks to the Emperor of our office, Peter McKeag - he's not Emperor for nothing!

Lions

One of my fondest memories from my further maths lessons back in my school days occurred when one of my colleagues brought to our attention the many ways a mathematician may trap a lion. In many a surreal moment I have stared wanly into the middle distance trying to recall exactly what was in the list, and the best I could do was simply remember with fondness that it was funny. Fortunately for me I need stare wanly no longer and I may trap lions to my heart's content for Bjorn has compiled a list of many ways to do this. Thank-you Bjorn! He also shares an amusing exam answer where a student took up the ages old challenge of finding x with great success!

Also I've followed the advice of Mr Goose and started using The TeXer for making small gifs of tex online - it's very handy, but I wanted to draw your attention to the excellent host site, called The Art of Problem Solving, claiming to be the world's largest online maths community. In particular I wanted to share my pleasure at their little geometric animations in the bottom left hand corner of the site as I think they are wonderful, I particularly like this one (which I have stolen (!) the end result of from their excellent site ):

P.S. Peter Woit provides yet another excellent link to online lectures, this time by Penrose, Weinberg, Maldacena amongst others at the Perimeter Institute. Peter was referring, in particular, to the emergence of space-time talks which can be found at the bottom of the list on the left, and one of the talks is by Seth Lloyd, the views of whom have been recently commented on by Lubos Motl.

My first journal club

The enthusiastic group of postdocs here at King's have organised a journal club for all of us students and interested faculty. I've not been involved in one before and so it will be interesting to see whether or not we make progress as a group or not. Our topic to guide our reading is gravitational thermodynamics and hopefully we will look at attractors as well as more recent alpha' corrections to the entropy formula. But to start off today we began with a background review. Here was our suggested reading list (totalling 315 pages)

Black hole thermodynamics by Simon F. Ross

TASI lectures on black holes in string theory by Amanda W. Peet

The Thermodynamics of Black Holes by Robert M. Wald

Black Holes by Paul K. Townsend
An abundance of middle initials, which bodes well. We really went over some definitions, such as surface gravity for the Schwarzschild black-hole, null hypersurfaces, temperature, Hawking radiation (which we hope to look at more closely next week), event horizon area increase (and we drew the analogy with entropy, but no more than that) and the formula at the heart of black hole thermodynamics:
So we didn't get too far into our review in an hour, and already there was some disagreement in our club between those who want to push on towards the string theory point of view and the recent papers and those who want to get the fundamental concepts under control before moving on. I foresee a rocky ride ahead, but it will be a fun endeavour. So, for now, our journal club rides on...

Healthy Scepticism in the Ranks

Yesterday Andreas Recknagel gave our first mathematics colloquium of the year. We heard a very rapid overview of unification, string theory and conformal field theory that finished up with T-duality and mirror symmetry. He even showed us some "strings" he had in his pockets to describe the winding number. The talk was peppered with good humour the first occurred at the outset where he described "the string factory" to us, here are my notes on it:

Heterotic Geometries, all of them

This week George Papadopoulos talked to us about the results from his latest paper, The spinorial geometry of supersymmetric heterotic string backgrounds, with Ulf Gran and Philipp Lohrmann, from my office. I used to keep a pink penguin on the site as a tribute to Philipp, that one could poke and push off some ice while reading the blog. Happy days. Now I have to treat him with much more respect since he and his collaborators have made use of the fundamental procedure of the spinorial geometry programme (which I will describe below) to produce a list of all the possible background geometries for the heterotic string, up to multiplication by a compact group in some cases.

The talk itself began a little ominously on Wednesday when it was realised that our electronic projector was not available, and instead of us all crowding around George's laptop, he managed to give us a blackboard talk which was impressive both for its clarity and in that he hardly ever looked to his laptop for guidance. However one consequence of this was that hardly any complex equations appeared even though there must have been many more intended, and also the speed of the talk was very good for those taking notes. I wonder if this policy of losing the projector is not something we should take up full time at King's...

George began by motivating the study of the Killing spinor equations by looking at the Euclidean instanton bound. In 4-dimensions,
Where we have completed the square. The bound is saturated when,
When we take the minus sign in the above we have the self-duality conditions on the field strength. Now suppose we wanted a spinorial version of this construction. We would start by coupling the spinor to the field strength forming:
Reproducing the equivalent of the Euclidean action above we have another formulation for the instanton bound, but now in terms of spinors,
Normalising the bound is attained if, These are the supergravity Killing spinor equations arrived at by considering the instanton bound.

Having motivated the Killing spinor equations, George moved on to describing the formalism he has developed for helping to solve them. He took us through a 4-dimensional example so we could see the general approach. In 4-dimensions the spin representation is Spin(4) which is the double cover of SO(4), the Euclidean rotation group. There is an isomorphism Spin(4)=SU(2)xSU(2) and there are two different Weyl spinors, with two components in each, which transform under only one of the SU(2)'s. George then described the setting up of a real vector space, whose components will act as a space of forms. In two-dimensions we have two basis elements in the vector space (e_1,e_2). Mimicking the splitting of the Weyl spinors to transform under two different copies of SU(2), we set up a second copy of this vector space by "complexifying" it. The basis of forms is:
We have a basis of two even and two odd forms which corresponds to two different chiralities. If we explicitly write down the gamma matrices using our basis we can get some work done,
I have used a vee for the inner derivative which acts in the opposite way to the exterior derivative; it's destructive while the wedge is constructive, e.g. . These are all we need to solve the Killing spinor equations. We first note that the equation is unchanged under spin(4) transformations, upto a Lorentz transformation on the field strength. That is we may orient the spinor how we wish, in particular we may pick the direction 1 (the "Clifford vacuum" if you like) in the basis:
Now we may go back and look hard at our basis for the gamma matrices and write down the combinations that annihilate the vacuum. We use these to define a new (solution) basis:
We also have a set of antiholomorphic gamma matrices in this basis which are the complex conjugates of the above. Finally expanding out the Killing spinor equation, by summing over holomorphic and antiholomorphic indices, in this basis leads to some simple expression,
Recalling that the n index gamma matrices are just the antisymmetric combination of the n individual gamma matrices, we see immediately that the first term annihilates the Clifford vacuum. Carrying on thinking about this in terms of a basis of states is fruitful since we also see that the remaining two terms must vanish independently, since they create different "Clifford states". That is the Killing Spinor equations reduce to,
So we see from this walkthrough just how simple the equations can become. In particular one can learn about the geometry of a number of setups. In the latest work, linked above, the authors make use of the fact that the heterotic string background resembles a Riemannian manifold, to find all the stability subgroups for the possible numbers and types of Killing spinors. From which the geometry of the background is determined. So impressively it is claimed that all the M-theory geometries corresponding to the heterotic string regime without alpha' corrections have been found. Of course it is not clear what happens to the Killing spinor equation when alpha' corrections are included, but it seems like they will be altered.

SuSy backgrounds and M-theory corrections

It would be remiss of me not to point out the Vega Science Trust which has been recently highlighted on cosmicvariance by Mark Trodden; if nothing else go and watch the Feynman lectures available there. Elsewhere Seed magazine seems to be getting much blog support (see here, here and here). So jumping on the bandwagon I'd like to recommend the Seed magazine podcast so you can have "science is culture" articles wherever you take your mp3 player. In fact if you are keen on podcasts you should also listen to Berkley Groks.

This week Kellogg Stelle from Imperial College visited KCL to tell us about his work on corrections to M-theory at order {\alpha'}^3. In particular he described work which demonstrated how supersymmetry may be preserved by making use of a corrected killing spinor equation. Indeed one may work backwards and start with a corrected killing spinor equation and rediscover the corrections to the string background. The methods used for various supersymmetric backgrounds are based on the following papers written variously with Lu, Pope and Townsend:

Higher-Order Corrections to Non-Compact Calabi-Yau Manifolds in String Theory (Kahler manifolds)

Supersymmetric Deformations of G_2 Manifolds from Higher-Order Corrections to String and M-Theory (G_2 manifolds)

String and M-theory Deformations of Manifolds with Special Holonomy (Spin_7)

Generalised Holonomy for Higher-Order Corrections to Supersymmetric Backgrounds in String and M-Theory (Generalised holonomy)

If you want to learn more read through the first paper above, there are some surprising results. You might even be keen on thinking about the alpha' corrections and the group E10, or even their effect on entropy calculations. I'd write more but 'tis the season to be making postdoc applications and I really have to be seasonal, very quickly and as many times as possible. Ug, the drudgery.

A Silver Age in Black Hole Research?

Yesterday afternoon Harvey Reall from Nottingham University came to talk at Imperial College. The talk entitled Black Holes and Extra Dimensions was aimed at masters level students, of which, there was only one in the audience :( However it was a nice talk, and somewhat of a black hole history lesson and worth describing here. Lubos Motl has a report of a very similar talk by Reall which you can find here.

Harvey began by describing the "Golden Age" (so named by Kip Thorne) of black hole research which began in 1963 with the discovery of the Kerr solution, and supposedly lasted until 1973 when the macroscopic black hole entropy formula was discovered by Hawking. The two main achievements of the "age" according to Reall were:

1. The black hole uniqueness theorems
2. Black hole thermodynamics

The uniqueness theorems (for more information you can read David Robinson's "Four decades of black hole uniqueness theorems")in 4 dimensions are twofold; there are separate proofs for the non-rotating and the rotating vacuum solutions. The non-rotating solution is due to Werner Israel (1967) and a more recent proof by Bunting and Masood-ul-Alam (1987) and shows that the only non-rotating, equilibrium solution is the Schwarzschild solution (1917). The only rotating, equilibrium solution is the Kerr solution (1963) as shown by Carter (1971), Hawking (1972) and Robinson (1975). These solutions are described by one (M) and two (M,J) parameters respectively. Generalisations to include the Maxwell field also exist (the Kerr-Newman solution).

Reall spent some time motivating the consideration of extra dimensions. For those interested in string theory he simply said that it is, in his opinion, the best candidate for a theory of quantum gravity. He justified this by saying that the entropy macroscopic entropy formula is the only experimental data that we have for quantum gravity and that microscopic count of entropic degrees of freedom gives matching numbers. For those not so convinced by string theory Reall offered the AdS/CFT (Maldacena 1997) or as he called it the Gauge/Gravity correspondence. The gauge/gravity correspondence was described for the case of a 5D gravity theory in the interior of the cylinder (shown right) being equivalent to a 4D gauge theory on the curved surface of the cylinder - the edge of the cylinder is at infinity by some clever choice of coordinates and three dimensions have been suppressed out of respect for our 4 dimensional universe. In short Reall pointed out that some 4D gauge theories are equivalent to 5D gravitational theories and so we may learn more about QCD calculations by looking at higher dimensional theories.

Reall then moved on to talk about constructing 5D solutions from the known 4D solutions. He began with the black string which was constructed by adding an extra flat dimension to the Ricci flat 4D Schwarzschild solution: This is the black string, it is infinitely long and so has infinite energy. To avoid this we compactify the z direction by identifying z~z+2/piR, the geometry is changed to 4D Minkowski space crossed with a circle. Reall told us that the Black string This is the black string, it is infinitely long and so has infinite energy. To avoid this we compactify the z direction by identifying z~z+2/piR, the geometry is changed to 4D Minkowski space crossed with a circle. Reall told us that the Black string is classically unstable when the radius of compactification, R, is greater than 2M. This is the so-called Gregory-Laflamme instability (1993) and it's endpoint is unknown. However Horowitz and Maeda (2001) conjectured that the endpoint was the non-uniform black string, which has a sine-wave distortion of the event horizon as it moves through its z coordinate. Toby Wiseman showed that these exist using a numerical approach in 2002. The downside is that they lead to decreasing entropy, which is unrealistic!

There is a generalisation of the Kerr solution to D dimensions called the Myers-Perry solution (1986). It has some familiar properties in that it's event horizon has topology S^{D-2} and it is uniquely specified by its mass and its angular momenta (there being [(D-1)/2] angular momenta, where [] means drop the fractions). Another familiar property is that the angular momenta are bounded. Having described this much Harvey Reall asked if there were any other types of higher dimensional black holes, i.e. does the rotating black hole uniqueness theorem still hold in higher dimensions?

Harvey answered that he and Emparan had showed that there existed a different type of black hole in 5 dimensions (2001) - the black ring. This solution is a rotating closed loop of black string, whose gravitational collapse is held at bay by one of its angular momenta. Heuristically the gravitational force is balanced by the centrifugal force. Of course one wonders why a similar rotating black cylinder couldn't exist in 4D...to project to 4D one could set r=0, corresponding to zero mass, hence no 4D equivalent solution to the black ring, at least not in this way. The 5D black ring's second angular momentum is zero and the solution has only 2-parameters with topology S^1 cross S^2.

It transpires that for a certain range of angular momentum there are two ring solutions, one small and one large. So together with the Myers-Perry solution there are some regions of parameters where 3 solutions exist for the given parameters. The uniqueness theorem for rotating black holes is well and truly lost for higher dimensions. The non-rotating uniqueness solution does still hold in higher dimensions (Gibbons, Ida & Shiromizu 2002).

Harvey finished up by telling us about supersymmetric black rings (also known in some circles as: "The Hairy, Tiny Black Hole Donut Theory") which were discovered by Elvang, Emparan, Mateos and Reall (2004); Gauntlett and Gutowski (2004); and Bena and Warner (2004). You can listen to Reall talk about black rings here. The solution is now stabilised by a non-zero second angular momentum (this one rotates the torus about its second circle). The solution has 7 parameters: 2 angular momenta, 3 electric charges, 3 magnetic dipoles and one relation between them all. Also noteworthy is the observation that the dipoles are not conserved, so there are only 5 conserved quantities amongst the seven parameters. The entropy formula is consequently much more complicated than usual but despite this it seems that string theory can still be used to give a correct microscopic count of the solutions degrees of freedom (Cyrier, Guica, Mateos and Strominger 2004), although Reall had some doubts about the count since it seemed to imply that one of the two angular momenta was zero, contrary to the macroscopic solution.

In his final remarks Reall reminded us that the golden age of black hole research was started off by the discovery of the Kerr solution, and he hoped that the silver age would be kicked off by the discovery of the black ring. Personally I'm already worried about naming the third age, since the bronze age is already taken.

A Bridge to Higher Spin Theory and AdS/CFT

Last weekend I was pleasantly surprised when a friend phoned me and said he was in my neighbourhood and thought we could go for a drink. Unfortunately there were scheduled works on a bridge between where he was and where I live; I thought the bridge would be raised and he replied asking if that meant we were topologically disconnected... This was somewhat similar to how I felt yesterday at our weekly seminar, since the topic seemed to be "topologically disconnected" from my own small area of understanding. So in these comments I propose to try to build a small bridge to the beginnings of the subject matter discussed in the talk.

So Paul Heslop from DAMTP in the real Cambridge came to talk to the King's group under the title "On the higher spin/gauge theory correspondence" which is based on his work with M. Bianchi and F. Riccioni. Paul's talk was based mostly around their paper "More on La Grande Bouffe: towards higher spin symmetry breaking in AdS". Don't be put off by "La Grande Bouffe" it is the name of a film and it refers to an aspect of the theory where a higher spin field "eats" the entire chain of lower spin fields to acquire mass, these chains can be very long. The film of the same name, we were told by an anonymous member of our department, is about "three men and one woman" and the men all eat so much that they die! Via IMDB the plot is described as:

Four successful middle-aged men Marcello, a pilot; Michel, a television executive; Ugo, a chef; and, Philippe, a judge go to Philippe's villa to eat themselves to death.

It has 7.2 stars from 1225 reviews. So don't be put of by the term, which I believe is due to Massimo Bianchi.

The conjectured correspondence is that "the massless higher spin theory is holographically dual to a free gauge theory on the boundary". We can summarise it best using a picture given in Paul Heslop's talk:
If you wish to learn about the correspondence then you can read through the following papers of Bianchi et al:

"Higher Spin Symmetry and N=4 SYM" by Niklas Beisert, Massimo Bianchi, Jose F. Morales and Henning Samtleben

"Higher spin symmetry (breaking) in N=4 SYM theory and holography" by Massimo Bianchi

"Higher Spins and Stringy AdS5xS5" by Massimo Bianchi

However since there is a gap in my understanding, I thought it would be constructive to find a brief paragraph or two to express the formative ideas behind Vasiliev's higher spin theory, if I can. However a better option would be to listen and see pictures from a talk by Vasiliev here, where you will hear him commence by describing the totally symmetric massless free fields of Fronsdal (1978) and de Wit and Freedman (1980) where the bosonic case contains a field with s symmetrised indices which is double-traceless (i.e. if you contract two pairs of its indices it is zero). There is a uniquely associated action which is chosen by requiring that some action containing terms up to second order in derivatives of the field is gauge invariant. There are some familiar gauge invariance principles for s=1 (Maxwell) and s=2 (gravity) fields and the essence of higher spin theory is the question of whether there is a unifying gauge symmetry that exists for other higher spin fields as well.

What are the connections with strings and supergravity I hear you cry? Well Vasiliev goes on to say (in the video above) that while there is a limit on the spin of the massless particles in a d-dimensional theory (s=d-2) there is also a corresponding limit on the number of supersymmetries (e.g. he draws a parallel between the s<=2 and N<=8 in 4-dimensions). He says that this is "practically equivalent" to the limit on the number of dimensions of supergravity (d=11) and says that if one wishes to consider theories beyond supergravity then one might start by wondering what happens when one includes massless spin fields of spins higher than those in D=11 sugra. Further motivation comes from the Stueckelberg symmetries of the superstring which are similar to spontaneously broken symmetries of higher spin gauge symmetries. As well as from the work of Sundborg and Witten, arguing for a nonlinear theory with infinite higher spin fields in the bulk.

So there you have it a small bridge to travel over and go and study higher spin gauge theory. A couple of further papers to help you on your way towards the triangle above are:

"Higher Spin Gauge Theories"(be warned this is a link to a 205 page pdf), Volume 1 of the proceedings of the Solvay Workshop, a compilation of work in various areas related to higher spin theories.

"Notes On Higher Spin Symmetries" by Andrei Mikhailov

It transpired last weekend that the scheduled roadworks were not happening, the bridge was down, and just like this week's seminar experience my friend and I were topologically connected after all, and we went and had a merry afternoon in Greenwich.

Black Hole Attractors and Entropy

On Friday, Atish Dabholkar from the Tata Institute of Fundamental Research, visited Imperial to talk about microscopic entropy counts, small black holes and the use of the attractor mechanism. This is a very interesting topic, and arguably the area where string theory has had its greatest success so far.

So let's recap: In 1973 Bekenstein suggested that the event horizon was proportional to the black hole entropy, shortly after Hawking became convinced of this and produced his famous equation relating the entropy of the black hole to a quarter of the event horizon. However, from statistical mechanics we have become accustomed to being able to understand entropy as a count of the degrees of freedom of a microscopic system, yet from general relativity we expect all material to fall towards a singularity, sometimes a point and sometimes a surface behind the event horizon. All degrees of freedom as we understand them classically are suppressed at the singularity so how to account for the entropy microscopically is quite a puzzle, we are led to believe that there are some hidden degrees of freedom. This is an ideal situation to turn to superstrings (at least if you are predisposed towards string theory), living in ten dimensions gives them six dimensions in which to hide such degrees of freedom from us four-dimensional beings. And indeed Vafa and Strominger were able to make a microscopic count for a five-dimensional black hole using string theory that agreed with the macroscopic entropy coming from the event horizon area. The idea is that we can consider in 10-dimensions coincident D5-branes, a D1-branes and strings going between the two types of brane, and the excitations of the strings account for the degrees of freedom (if you want to read more about this picture at an introductory level then chapter 16 of that wonderful purple book by Zwiebach is recommended). This is then compactified on a T^5 to give a point, corresponding to the singularity in the 5-dimensional spacetime. In fact this construction corresponds to the 5-dimensional Reissner-Nordstrom black hole, as can be seen from the algebraic approach taken by Clifford Johnson in his slightly less purple book D-branes. There are a number of equivalent dual pictures and one of the most illuminating in terms of finding a geometrical reason for picking this combination of branes and strings is described in a very readable paper by Samir Mathur, The fuzzball proposal for black holes: an elementary review. Mathur entices us to consider an M2-brane dimensionally reduced on a spacelike circle in the z-direction to give a NS string in the IIA theory and then further compactify our setting by wrapping the NS string around a circle in the y-direction. Now go back to the 11-dimensional picture and think about the event horizon of the M2, it is shrinking because the M2 tension is wrapped around two closed loops and pulling them tight. The horizon is shrinking to zero, and we find that we have zero macroscopic entropy. We aim to stabilise the 11-dimensional horizon and gain an entropy that isn't disappearing. This will mean that we have a stable extremal, or BPS, black hole, one that isn't radiating and shrinking. Again let's go back to the 11-dimensional M2 picture. The M2 is radiating, so that had there been any other compact dimensions transverse to the M2 it would try and excite them and blow them up. Aha! So let's compactify some of these other dimensions and wrap another brane around those and see if we can't balance the tension of the second brane with the expansion caused by the first brane and vice versa. We pick an M5 brane and place it transverse to z in 11-dimensions, giving us a NS5-brane in IIA, we wrap this around T^4 (transverse to the NS1) and S^1 (in the y-direction). Now this turns out to be enough to stop the shrinking of the z-direction in the 11-dimensional view, but both branes are wrapping the y-circle and it is shrinking. We may excite the y circle by adding momentum charges around the circle which have energy proportional to 1/R, so they have lower energy for larger R and keep the y-circle non-vanishing. Phew. Now we have three charges coming from the NS1-NS5-P system (which may be dualised to D1-D5-P) and a stable horizon. That this is a BPS state means that we can count the degrees of freedom for different values of the coupling constant g and still expect the count to stay the same. So this is a heuristic approach outlined by Mathur for picking this special system. For the actual counting I refer you to some of the literature here, here and here. And what about other black holes, in particular the Schwarzschild black holes: can we find a similar stringy construction for counting the microstates? Well, yes, we can see for example Englert and Rabinovici.

But what about that NS string we considered alone earlier, our arguments told us that it had zero entropy, and yet it still contains microscopic degrees of freedom, so what's going on? Atish Dabholkar started his talk by asking us whether the S(Q)=klog[\Omega(Q)] was absolutely correct and if we could compute corrections to both the macroscopic and microscopic counts of the form:

S=a_0A(Q)+a_1log[A(Q)]+a_2/A(Q)+....
klog[\Omega(Q)]=b_0A(Q)+b_1log[A(Q)]+b_2/A(Q)+....

He pondered whether we could compute the a's and the b's and did they agree, and then told us that for a class of BPS N=4, D=4 black holes this can be confirmed. He said that on the macroscopic side one must take into account higher derivative corrections to the action (i.e. graviton scattering) and work in the thermodynamic limit for the association between entropy and degrees of freedom to carried over exactly from statistical mechanics. If this approach is sensible, then we would find that our NS string would have contributions to the entropy but not at the first order.

Atish outlined his approach, or ingredients as he put it:

1. Action: N=2 sugra + topological string
2. Entropy: Bekenstein-Hawking-Wald formula
3. Solution: via the Attractor mechanism
4. An ensemble: some Ooguri-Strominger-Vafa mix of charges

He told us he would work with small black holes (= only two charges in the ensemble), where the counting can be done exactly and the classical area vanishes (as we saw above), and so corrections are essential. The approach is detailed in his 4-page paper Exact Counting of Black Hole Microstates and in his talk he commenced by telling us about how to regularise black hole backgrounds by using "stringy cloaks" and this is described in his 10-page paper with Renata Kallosh and Alexander Maloney entitled A Stringy Cloak for a Classical Singularity (you can watch a talk by Andrew Maloney on this paper here). Since the details of the talk are not suitable for blogging I will direct the interested reader to the other relevant and much longer papers written with Frederik Denef, Gregory W. Moore and Boris Pioline, the 35-page Exact and Asymptotic Degeneracies of Small Black Holes and the 103-page Precision Counting of Small Black Holes. Also of interest will be Ashoke Sen's Black Hole Entropy Function and the Attractor Mechanism in Higher Derivative Gravity, and you can see the slides and listen to a related talk given by Sen here.

Sorry to trail off without describing the details but one they are tough, and two I am tired. All comments on this approach and joyous sonnets praising (and explaining)the usefulness of the attractor mechanism are welcome. There, and I didn't even mention supersymmetry once, oops.

Update: Check out Jacques Distler's post about David Shih's work on Ooguri-Vafa-Strominger constructions and see also his comments on Dabholkar et al's work and small black holes.

Hawking on Richard & Judy

One day's notice for those of you in the UK that Stephen Hawking will be appearing on tomorrow's (12th October) Richard & Judy show, probably to talk about his new book. This is one of the most unlikely pairings I can imagine and should be fun to watch.

Nobel Prize 2005

The Nobel prize for physics this year has been awarded to:

(1/2 of the prize) Roy J. Glauber for "for his contribution to the quantum theory of optical coherence",

(1/4 of the prize each) John L. Hall and Theodor W. Hänsch "for their contributions to the development of laser-based precision spectroscopy, including the optical frequency comb technique."

Many hearty congratulations to them!

Update: the BBC have a short story on the award, and there are also comments from Lubos Motl and Peter Woit.

Topological Mass Generation

So perhaps you thought the Higgs mechanism was the only mechanism for mass generation in four dimensional spacetime? Probably it is, but Roman Jackiw, co-discoverer of the axial chiral anomaly with Bell and Adler, spoke at Imperial College yesterday about an alternative and elegant method to generate a 4-dimensional mass term. Roman first described to us the three-dimensional model where a Chern-Simons term can be added to the Lagrangian to generate mass, but told us that his motivation would come from the Schwinger model in two-dimensions. In the Schwinger model massless Dirac fermions are added and then eliminated in order to generate a mass. With hindsight Topological Aspects of Gauge Theories by Jackiw, which is to appear in the Encylopaedia of Mathematical Physics would have been a good article to read before attending this seminar.

Roman went through the original model and then repeated the analysis using a number of dualised terms, he referred to this as going "towards the topological model". In particular he highlighted that the field acquires a mass due to the presence of a chiral anomaly in the axial vector current and leads to a massive pseudoscalar; the pseudoscalar being dual to the two-index field strength as well as being proportional to the divergence of the axial vector current.

Now Roman's aim was to take this two-dimensional model, made out of purely topological terms, and then write out the equivalent expression using the four dimensional topological objects. He said that he would call this topological mass generation since now he would refer to the terms we had before with their topological names.

In two dimensions, using the dualised terms, a pseudoscalar crops up that is the Chern-Pontryagin density, P, and the dual of the potential field, C^\mu=\epsilon^\mu\nu A_\nu, is the two-dimensional Chern-Simons current. These are suitable quantities to take across to four dimensions, however it turns out to be a requirement of the method that the dual of the axial current must be a conserved quantity, and this can be guaranteed to occur by adding two fields, added in the form of Lagrange multipliers to the dual Lagrangian (I omit the details here unfortunately because I still haven't opted for a way of putting TeX in these posts). Surprisingly when one does this in order to conserve the dual axial current, one obtains a gauge invariant dual Lagrangian - the two go hand in hand. The generalisation of the Schwinger model to four dimensions is now straightforward, and is carried out by using the four-dimensional topological terms. Roman finalised by mentioning two shortcomings of this approach, the first being that the anomaly producing dynamics has not been specified and as such this model presents a phenomenological model of mass generation. The second shortcoming was the resulting dual Lagrangian was a dimension eight operator, and this, I am told, presents difficulties for renormalization. However on the positive side the specific contribution needed for the anomaly appears in the expansion of the Born-Infeld action to quadratic terms. Furthermore Roman pondered whether it might not present a phenomenological description for the elusive \eta'. Roman reminded us that the \eta' is the ninth goldstone boson suspected to arise by promoting an SU(3)xSU(3) symmetry to a U(3)xU(3) symmetry. This topological mass generation if it were indeed applicable to the \eta' would give a numerical prediction of the \eta' mass. For some notes about the mysterious \eta' see here. Apologies for any mistakes, one day I will read the much-recommended book by Zee and learn some QCD. Now I've written it here I just have to do it...

Horizon on Hawking

Last night Horizon was on the well chosen topic of information loss paradox in black holes. It chose to cover the story as Stephen Hawking's "greatest ever mistake", drawing unbidden parallels with Einstein's greatest mistake. It was hard not to get excited about a popularization of such a technical nature, and I felt somewhat let down when we were treated to the usual combination of ominous voice-over (why, oh why, must science be presented as if it's a horror movie?), violins playing purposeful music, dazzling graphics, and vague presentation of the story. In fact the story was shifted away from physics to one questioning Stephen Hawking's scientific reputation leading the Horizon team to entitle their programme not "The Information Loss Paradox" but "The Hawking Paradox".

I admit though that, before I watched the programme, I was excited about it all day; in the best of all worlds I was hoping to hear some commentary on Hawking's most recent paper, perhaps even some insights that might help me understand it. But alas not. The programme aired at 9pm on BBC2 yesterday, and my spirits immediately sank when the announcer introduced it as "the reputation of the world's most famous scientist at stake". The first images we see are from a beach and there's a wall with at least 6ft high graffiti on it, and the largest graffito of all is of Hawking's equation relating entropy and event-horizon area. Perhaps this was also meant to draw parallels with graffiti of E=mc^2, who knows? The voice over begins, and the camera ranges over the beach to an astrologer:

"What if the world were so strange we could never hope to understand it and science was wasting its time? It sounds like the sort of thing a mystic might say but this was a suggestion made three decades ago by the most famous scientist in the world, Stephen Hawking."

From then on one had the idea that the scientific story was going to lag behind the human story, but, for pity's sake, why?

The introduction focussed on Hawking's celebrity, with Kip Thorne saying of him:

"He's absolutely unique, and I think he has been a very important person in both the intellectual and the cultural life of the past century."

These fair comments were countered by the voice-over's,

"But recently doubts have been expressed by some physicists about Hawking's scientific reputation."

Thereby initiating the main story being addressed by Horizon, that perhaps Hawking ain't so great. Frankly this appeared as unfounded, unsupported and scurrilous journalism used to appeal to a wider audience, and at no stage were any of Hawking's conributions to physics not related to information loss discussed.

The information loss paradox was described as the result of a black-hole evaporating to nothing leaving behind only thermal radiation, i.e. carrying no information. That there would be a problem even if the black-hole didn't disappear was not made clear
(There is clarification about where this is a concern from Christophe Galfard in the comments). Without recourse to quantum mechanics this was described as a violation of one of the most fundamental principles of physics, that information is never destroyed. The voice over spookily summarised,

"Effectively bits of the universe are missing...nothing science knows not even our memories could be trusted."

Lawrence Krauss commented, probably to the delight of the Council for making Science Scary who seem to be in charge of Horizon,

"...at its most extreme scale what it means is everything you come to know and love would ultimately disappear."

This scary comment went without any guiding timescales.

Cue Leonard Susskind who was presented as Hawking's adversary in an immense intellectual battle. Susskind described how he felt a need to resolve how it was that one could watch someone cross into an event horizon and potentially be pulled apart, while the same person would feel no great change as they themselves fell across the horizon. Ah, a good old-fashioned change to Eddington-Finkelstein coordinates, at last some firm ground. The voice-over's interpretation of this coordinate change:

"The same equations were saying that someone could be both dead and alive."

Hmph. Susskind described his resolution that allowed both of these possibilities to coexist and resolved the information loss paradox: holography. That the black hole acts like an information projector and that anything that falls into it has its information "beamed" onto the lower-dimensional event-horizon, thus avoiding losing information inside the event horizon. Although quite what was going to happen to the information when the black hole evaporated was not addressed. Susskind's belief's were presented as being vindicated by Maldacena's paper, Eternal Black Holes in AdS. And finally the programme concluded after the Dublin conference where Hawking conceded that information was preserved. So, no chance of an explanation of the sum-over-topologies approach, ho-hum. There is some commentary by Lubos Motl on the paper Information Loss in Black Holes, and if you are interested in holography you could read TASI lectures on the Holographic PrincipleTASI lectures on holography by Bigatti and Susskind.

Of course despite my disappointment with the lack of theory, the human story was appealing. There were some very nice pieces of footage of Hawking working with his students. In one shot, prior to adopting his synthesiser, Hawking is seen talking to what looks like a seminar with the help of a student, Chris Hull. Chris Hull says that they happen to have a model of the universe with them and pulls out a cylinder and puts it on a table in front of the audience. Hawking makes some comments and grins, the student scratches his head and then turns the cylinder the other way up. It is identicle both ways.

Also, there were some encouraging comments about the trials of a student from Christophe Galfard, who, contrary to my earlier scandalous comments, has pointed out that he does not work in the signature (+---), described the start of his PhD with Hawking, saying:

"For the first year-and-a-half every sentence of Stephen's took me about six months to understand."

And of reading Maldacena's paper:

"I took a little while to read it, a little while being about a year-and-a-half."

Again: here, here!

The show ended with Hawking saying:

"I have no intention of stopping anytime soon. I want to understand the universe and answer the big questions, that is what keeps me going."

At no point did the programme mention the word string, nor topology! Is this really the best way to promote science to a popular audience? Could it not be done with at least a little humour, and less of the portentous voice over? Maybe even less of the human-interest story? After all the science is fascinating if communicated well. Oh for a more perfect world.

Not with a whimper...

The BBC news website has a story entitled Black holes start with many bangs. Observation of multiple gamma ray bursts by the Swift observatory, designed to detect very short bursts, improves upon previous recordings of a single decaying burst. The bursts are expected to be associated with black hole formation, radiation from infalling material. But from the tone of the article it seems the astronomers are not clear about the causes yet. While you're thinking about black holes go and look at Jillian's Guide to Black Holes, if you haven't already done so, it is a beautiful site.

Also in the news recently is a new "three line" putative proof of Fermat's last theorem. Alexander Ilyin, a "doctor of technical science" who works in automated data processing in Omsk, unveiled his proof at a press conference on 23rd August, and according to this Pravda article

"colleagues in Omsk believe Alexander's proof is flawless and simple"

Furthermore the article continues,

"Omsk-based scientists and journalist have not found any errors so far"

Journalists are obviously of a much higher calibre in Russia. A follow-up article that fails to make it plain whether or not the proof has been withdrawn, but covers the popular history of Fermat's last theorem very nicely is here, and a discussion thread here.

Thanks to the Mighty Emperor of Room 102, Peter McKeag for pointing out this story.

The Joy of Ping

I have been learning about trackbacking, and as the observant reader will note there is now a new trackback link beneath each post. So for those as uninformed as I was "trackbacking" is the name given to creating links to blog entries containing content relevant (hopefully) to the post you have just read. The purpose is really to keep a record of links that didn't make it into the post, principally because the links were created after the post. If you find that last sentence confusing, then don't think twice about going to see the movie Primer (incidentally, I watched it yesterday and found it very confusing, but I'm enjoying thinking thorugh its time-travel paradoxes, so forget my comments and go and see it and then tell me what happened). In short it is a blogger's duty to trackback to articles that have inspired comment.

How does one do this? Well, first you can only trackback to an article if you include a link to that article in your main post. And second you can only do this on blogs that support trackbacking - so standalone blogger blogs which do not support trackbacking have to use an external program, I am using haloscan. If trackback is supported then beneath a post will be a trackback link that gives a URL to ping. In essence, pinging means sending some information to another server to let it know you are there. One pings and is pinged, but one is never punged nor panged, one briefly can be pinging and one can certainly pong. If you keep a trackback-supported blog, then you can use your trackback software to ping other blog articles to let the world know you have something to say about that post. Some blogs have automated trackbacking (e.g. WordPress) where the software automatically pings every link in a post. This is almost enough to motivate a change of blog software...

Why all the sudden fuss about trackbacks and pings I hear you cry/sob? Well as you may have read here, here, here, here, here and here the arxiv is trying out trackbacking. On each abstract page there is now a trackback link, if any exist, so that it would seem that anyone in the blogosphere can comment on any paper. There is some manual checking of trackbacks so that supposedly only bloggers with legitimate comments about papers can add a trackback. It remains unclear how a comment may be judged legitimate, but probably a commen-sense test will suffice. Apart from this it would seem there are few safeguards and I can't decide if this is a good thing or a bad thing. For example, in the past I have attended seminars and attempted to understand a particular paper from the arxiv. Often I have understood a little of the beginning of a paper and have posted comments about that on this page. Now it seems I, along with others, will face the dilemma of whether sparse comments on a paper warrant a trackback to the abstract page of the paper. My feeling is that all legitimate discussion is positive and merits a trackback to the arxiv. I imagine that, if it takes off, trackbacking on the arxiv will offer a connection to debates about the papers content as well as earnest readers' descriptions of their attempts to understand (parts of) papers. To me it sounds utopian, but we'll have to see how it works out. Furthermore it may make the physics blogosphere lose its orbit, so to speak, after all will anyone who wants to make a comment about a paper and have it recorded on the archive also have to keep a blog? Recently there have been several bloggers sending posts from the midst of a conference, and at least one case of specific conference blog. Inclusion of comments from such blogs on the archive would seem to be a very exciting development since these are usually fairly technical, and hopefully useful. Perhaps this will motivate conferences to keep such blogs, and give an indirect link from the archive, via a blog entry, to footage or slides from relevent talks at a conference. Well let's hope so.

Elsewhere, the debate about the greatest physics paper ever trundles on, and still no-one has argued on grounds of simple beauty in favour of Kaluza's 1921 paper about the fifth dimension! Well except yours truly that is. Nevertheless similar to the BBC's series of greatest ever lists, cosmicvariance's lists have begun to hyperbole. Now the debates for the greatest ever physics textbook as well as the greatest popular science book are in full swing. Also Lubos has posted an updated link to the video footage of the talks from Sydneyfest. Also as reported here, here and here a second physics blog has become a book(let's not forget this trend was started by Lieven Le Bruyn)! Peter Woit's Not Even Wrong will be available in UK bookshops from 16th March, 2006. It promises to be an honest review of the toughest problems faced by string theory, and probably a critique of studying string theory with blinkers on. There has been some discussion about the merits of a non-string theorist writing a popular science book about string theory, but you can read them on Not Even Wrong the blog and, probably, the book in due course. Have no fear, I foresee no situation where this blog will become a book, although Tangent Space wouldn't be an awful title for a sci-fi novel (all suggestions for plot are welcome, in return for an earnest acknowledgement in the foreward)...

The 80th Best University in the Whole World!

King's College London is the official 80th best university in the world at least according to the recent top 500 list. Peruse the top 100 here, this link has been gleefully hijacked from Goosania.

Also in blogland is Clifford Johnson's attempt to follow where the BBC lead by finding the top 5 greatest physics papers ever written as decided by the readers of Cosmic Variance. I've taken up the challenge and nominated my favourite(s), I'm really hoping I can get fifth place on the list for Kaluza's 1921 paper where he discovered the fifth dimension :) But I suspect a campaign for Kaluza enacted solely by me may not cut the mustard but we'll see... also there have been no string/supergravity papers so far, which ought to be rectified.

There are other lists on the web, but one of the most curiously titled is Forbes list of the best places to die. Perhaps also of interest are the top 200 sci-fi novels (there are plenty of lists like this though, such as this one), Physicsweb's readers' top 20 equations, and there's "The Top 100 Things I'd Do If I Ever Became An Evil Overlord".

It's Oh So Quiet...

Things are quiet around here right now, no seminars, students and lecturers are away (avoiding the liquid sunshine) and nothing is stirring not even a mouse...so I have no notes to put up here.

However, the football season has commenced again, so it is a very exciting time, especially if, like me, you are a Queen's Park Ranger's fan as QPR have hit the headlines two weekends on the trot for non-football reasons. Last weekend, QPR fans were taunted by Hull fans about the London bombings and yesterday Gianni Paladini, a director at QPR, was forced at gunpoint to sign a piece of paper detailing his resignation from the board. Well this is sensational stuff and one really has to wonder who would do this and why, after all Paladini as a major stakeholder in the club has invested considerable amounts of money and also been pivotal in recently helping QPR to sign the defender Milanese. In short one would think that fans would appreciate Paladini's work, but also one would think that only very committed/insane fans would be driven to such rash actions. So something is amiss. Nevertheless, on the pitch, QPR have made a good start to the season, joint top in the Championship, and our legendary manager Ian Holloway is continuing to make football more fun, this week he summarised his pre-match team advice as "I told them to be awful." Let's hope he reaches the heady heights of this post-match interview again this season.

But even in the wilderness of summer in London there are plenty of physics links still that can be posted. First and most importantly the videos from LMS symposium Geometry, Conformal Field Theory and String Theory have started to appear online here. The organisers Patrick Dorey, Peter Bowcock and Katrin Wendland have done a fantastic job in collating all the videos so far and have even provided us with some photos of the symposium. In fact, for the curious, there's even a photo of me (I'm on the right) stuck in a castle window; at this point I am halfway through a tour of Bamburgh castle and am looking out the window and seeing the leader of our group (the one with the camera and the watch) a long way away and I'm wondering whether I'm being left behind... but it turns out, from the photos, that they were heading down to the beach and skipping the tour. There are also a number of other conferences that have provided media from their talks online (many of these come via Peter Woit's Not Even Wrong), so you can sit at home (un-jetlagged) and feel like you went to a lot of conferences, these include:

Strings 2005 - sound and slides.

Advanced Summer School on Modern Mathematical Physics in Dubna - A very impressive collection of introductory talks.

Mathematical Structures in String Theory at KITP - this runs from 1st August until 16th December and already there are videos available, and there is even a devoted (and secure!) weblog.

The SLAC Summer School: Gravity in the Quantum World and the Cosmos - videos are available under the titles for each talk.

Simons Workshop in Mathematics and Physics 2005 at Stonybrook - Vafa, Berkovits, Witten, Maldacena et al can all be listened to (slides are not generally available so you might have to listen very carefully...although some talks are close to those at Strings 2005, so some comparison is worthwhile)

A talk by Lee Smolin on Loop Quantum Gravity (from May 2005 with an astrophysics leaning - for the interested there are a host of astrophysics talks in the same directory)

The perfect quiet of this summer is well suited for the Ashes, however in case one thought that the genteel nature of a cricket test match might not be condusive to competition please see this violent yet thoroughly amusing game involving much Ozzie bashing on the Channel 4 website.

P.S. Please don't miss Lubos Motl's $3 challenge to disprove that Amazon, one of my favourite companies, are run by "crackpots" who are only allowing positive reviews of pseudo-science books which masquerade as science.

The End of the Road

Well we've reached the end of the LMS symposium in Durham, and I, for one, am really looking forward to going back home, and thinking about my own work problems. That said it has been a lot of fun to be here, and I may even try and learn something about derived categories off the back of all the talks related to them, and the enthusiasm of the categorists. I'm feeling pretty tired today, so I'm just going to list the last set of talks, starting with yesterday (a cold and miserably damp day).

In the morning the key-note speaker was Tom Bridgeland from the University of Sheffield, another of the enthusiastic categorists mentioned above, and he was talking under the title: "Spaces of stability conditions". He used words such as bounded coherent sheaf, topological B-model, elliptic curve, the Mukai transformation, T-duality, topological conformal field theory, Michael Douglas' Pi stability condition, Fukaya categories, special lagrangians (or slags), Richard Thomas and the McKay correspondence. Somehow all these words were related, and despite Tom Bridgeland being an excellent speaker (I do have a very good set of notes to work with from this talk), I'm afraid I know too little about algebraic geometry to be able to understand the topics. It has been suggested that a good place for me to start would be Serge Lang's book, "Introduction to Algebraic Geometry", and I'm giving it some consideration, although, at £364.27, I don't think I will be buying a copy any time soon. I believe many of the ideas discussed in the talk can be found in Tom Bridgeland's papers "Stability conditions on triangulated categories" and "Stability conditions on K3 surfaces".

In the afternoon we had a talk from Alexei Bondal entitled "Derived categories of toric varieties", and a second key-note speaker in the form of Ron Donagi who spoke about "Geometric transitions, Calabi-Yau integrable systems, and open GW invariants". Ron Donagi's talk was based on the papers "Geometric transitions and integrable systems" and "Geometric Transitions and Mixed Hodge Structures". After these talks we had a wine reception and a seven(!)-course banquet, which might explain some of my lethargy today :)

This morning we heard from Boris Dubrovin who gave the last talk of the symposium to an audience suffering from the morning-after effects of the banquet (principally the wine's effects) under the title "Frobenius manifolds and integrable hierarchies of the topological type". I refer the interested reader to his paper "Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants" for a flavour of the talk.

Now I have an afternoon to work in Durham and will catch my train home tomorrow, at which point I will catch up on my sleep. So ends my missives from the front here in Durham :)

Durham Talks Online Already!

A short comment to say that some of the pdf's of the talks so far at the LMS workshop in Durham are now available online here. I expect more will be added, along with copies of the student posters in due course, so keep checking back.

Generalised Geometry, Oscillating Integrals and Gauged WZ Terms

Today we have had a series of talks half of which were concerned with generalised geometry. Nigel Hitchin was due to speak this morning but was unable to due to illness, but he sent along his slides in his absence and Chris Hull and Richard Thomas filled the gap and made a very good presentation of his talk. The talk was entitled "B-fields, gerbes and generalized geometry" and the first half was a survey of the recent progress in the generalised geometry programme (see this related post about an introductory talk I saw given by Marco Gualtieri, a former student of Hitchin's). The second talk was concerned with looking at the different types of geometry classified by the programme, and was presented in by Richard Thomas. The slides from both parts are available online (part 1, part 2). Since much of the talk can be understood best by reading Gualtieri's thesis I will not say much apart from commenting on how well the two speakers did presenting someone else's slides. It really was impressive, bearing in mind they only had two days to prepare for it. Of course Richard Thomas did take advantage of the situation in order to add comedic value to his presentation, for example proclaiming that one of the slides was so straightforward that he was sure all of us in the audience understood it and so he wasn't going to spend any time talking about it (with a big grin), and more of the same throughout. In all it was a sterling effort from the two stand-in speakers.

After lunch, Claus Hertling, talked to us about "Oscillating integrals and nilpotent orbits of twistor structures", followed by Chris Hull's second talk of the day entitled "Generalised Geometry and Duality" based on his paper "A Geometry for Non-Geometric String Backgrounds". Hull's talk was probably the most accessible talk of the meeting so far for those of us with only an introductory background in physics.

Hull commenced by motivating us that a special approach to the geometry of a spacetime containing strings was needed. He did this by reminding us that the string excitations contain gravity and so strings have the possibility of altering the background spacetime. From there Hull discussed T-dualities which interchange the winding(string)/wrapping(brane) modes with momentum modes, commenting that compactifications on mirror symmetric Calabi-Yau manifolds leads to the same physics but usually on different geometric backgrounds. The picture he wasnted to analyse was whether it would be possible to combine the two geometric backgrounds, so that the whole geometry under mirror symmetry is unaltered along with the physics. His proposal began by doubling the coordinate manifold and using one copy of the coordinates to express the physics in terms of the degrees of freedom coming from the momentum modes, and the other copy of the coordinates to express the same physics in terms of the winding modes. The extra degrees of freedom were to be halved using a set of duality conditions relating the fields in the theory, e.g. dA=*dA'+... and the actual spacetime coordinates used to specify physics were to be singled out by a choice that Hull called polarisation. Since this proposal doubles the tangent space and is a further doubling of Hitchin's generalised geometry, Hull suggested the procedure might be called generalised generalised geometry, but then rejected this for the pithier T-fold geometry. The two sets of coordinates were to be glued together and the transition functions would be T-duality functions. Hull asked the question whether one would be able to patch together the sets of coordinates in this way to give a spacetime manifold and then told us that in general it would not be possible. The end picture was that while local spacetime would be covered by a coordinate patch, globally the manifold structure would be lost, and Hull seemed to be suggesting that doing away with the global spacetime manifold was not such a bad thing, if it meant that there was a better equivalence between geometry and physics. It should go without saying that this was my understanding of the broad picture of Hull's talk, that I may have got the wrong end of the stick, that Hull's arguments can be found in his paper, and that if anyone (especially those who have heard this talk) have any comments/amendments then I would be grateful if they posted them as a comment :)

After the coffee break, where I drank my fifth coffee of the day and got hold of some of the precious chocolate chip cookies that the organisers have been supplying us with, José Figueroa-O'Farrill gave a talk on "Gauged WZ terms in sigma models with boundary" which was based on his paper with Noureddine Mohammedi, "Gauging the Wess-Zumino term of a sigma model with boundary". Before commencing his talk José told us about the new research partnership ERP, Edinburgh Research Partnership and asked us to visit their website, in particular for the vacancies currently available. So consider this information dutifully passed on.

As if five talks weren't enough for one day, we were treated to an extra evening talk after dinner at 8pm entitled "How to Knit a Scarf" presented by Alastair King. Little did I suspect, as I should have done, that this wouldn't be a workshop and there was no wool involved :) Indeed it was a gentle (by the symposium standards) category theory talk, giving the physicists in the audience a gentle appreciation of the "natural" approach of the category theorists. A scarf turns out to be a quiver diagram composed out of many copies of three nodes (A_3) arranged in a triangle and with arrows having an anticlockwise orientation on the basis diagram. It was very colourful, and looked like it would be fun to work with, but that is the limit of my appreciation at the moment :( Alastair King also modified Terry Gannon's comments earlier in the week drawing a comic parallel between categorists and beavers to a quote of his own that ran "Category theorists are not like beavers". The surreal debate trundles on, and I live in fear of what will happen when category theorists discover the jumper.