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.
I am here for Eurostrings 2008, a smaller, quieter version of Strings, but which is packed with excellent speakers and an interesting crowd of participants. 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).
We began the day hearing Ashoke Sen talking about dyons in N=4 as discussed in his recent papers here and here. He described to us the protected index associated to BPS states, labelled d(Q,P). Here Q is the electric charge and P the magnetic charge. It is the number of BPS states weighted by , where 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 BPS states may decay into 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: , 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 and (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 duality. Starting with the near horizon geometry of a black hole and then analytcally continuing to the Euclidean solution one finds the 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:
By the AdS/CFT correspondence one can exactly calculate the partition function for the CFT:
Where is a rescaled ground state energy. Now the two expressions may be equated and the black hole entropy examined.
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 here. Pierre Vanhove, minus his infamous cow bell, spoke next on the no-triangle hypothesis (update: why not read Lubos' analysis of the situation) for SuGra, which is, of course, just 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 . Pierre finished enigmatically by telling the audience that if is divergent he bets that it diverges at 9-loops. He didn't say how much he bets.
In the afternoon, following a sparse lunch of soup and a sandwich, Hirosi Ooguri 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 here. After Ooguri, Marco Zagermann told us that 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 here. Finally Ki-Myeong Lee talked about "New" 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 here). 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 here.
At the end of the day we had a reception hosted at the Academy of Arts and Sciences, of which Robert Dijkgraaf 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".
After the reception I spent a nice hour wandering around Amsterdam in the sun.