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Low-functioning pinhead...
June 29, 2004
Strings 2004, Day 2
Sen gave a very beautiful talk on 1+1 dimensional noncritical string theory. He worked out the relation between the infinite number of conserved charges of the Matrix model and the infinite number of conserved charges of the continuum theory. This relation was known at a decade ago. Sen’s contribution was to generalize the formula to nonzero .
He then went on to discuss the long-standing puzzle of the subject: where is the 2D blackhole in the Matrix model? Unfortunately (to my mind), he discussed the question at — which is to say, using the formulæ available a decade ago. The idea was simply to identify the state in the Matrix model with the same set of conserved charges as the blackhole (, for ). The “solution” is to have a very large number of fermions and holes, each with very low energy.
Much of the rest of the day was devoted to fluxes.
Kachru’s talk was a nice overview of developments in flux compactifications in F-theory.
In the afternoon, Graña gave a very nice talk about her work with Minasian et al structures and Hitchin’s Generalized Calabi-Yau manifolds.
The last talk of the day was by Ofer Aharony about the deconfinement transition in large-N gauge theories at finite volume. For small enough volume, the transition can (interestingly enough) be studied in perturbation theory.
For the free theory, the path integral reduces to a unitary matrix model (for the Wilson line around the thermal circle), and one finds a Hagedorn transition (for free N=4 SYM on ) at . The interacting theory is still governed by a Matrix model, one whose effective action is more complicated, but which can be computed in perturbation theory. The phase structure depends on the signs of the coefficients in this effective action.
June 28, 2004
Strings 2004, Day 1
Some photos from the Registration at the École Normale Supérieur:
The hall at the Collège de France is quite beautiful, but too small for the assembled multitude. Sacha Polyakov gave the first talk on his recent work on new gauge theories from strings on certain homogeneous spaces for supergroups (like ). His model is -supersymmetric. There are two ways to attempt to deal with -supersymmetry. One is to quantize covariantly, which is generally very thorny, made all the thornier here by the nonpolynomial form of his action. His approach is to fix the -supersymmetry, in which case one needs to check covariance of the quantum theory. He said that -supersymmetry implies conformal invariance, which I don’t think is true, and which, in any case, does not seem to be the issue.
View from my hotel window, dusk.
He ended with a quote from Carl Jung, which seems only appropriate.
Mike Douglas’s talk also included a quote. This one from the poet Paul Valéry,
Tout ce qui est simple est faux, mais tout ce qui ne l’est pas est inutilisable.
a wise statement, but I still fear that Mike is studying the statistics of the empty set (or very nearly empty).
My favourite talk of the morning was Walcher’s on his work with Hori on D-branes in Landau-Ginsburg Theory.
I didn’t get very much out of Vasiliev’s talk in the afternoon, but Witten’s question afterwards was very clarifying. The conjecture seems to be that Vasiliev’s higher-spin gauge theory in the bulk AdS is equivalent to a free-field theory on the boundary. Nontrivial interactions of the bulk theory are obtained when we look at correlation functions of multi-linears in the boundary fields. Or something like that …
Rajesh Gopakumar gave a very interesting talk on rewriting free field gauge theory amplitudes in a stringy fashion (motivated by the AdS/CFT correspondence (I,II). The result looks intriguingly like an integral over the moduli space of genus-g surfaces with n punctures. The idea is to take the integrand and try to reconstruct the corresponding string theory.
I’ve blogged about the -maximization conjecture before, but Ken Intriligator’s talk was a really nice summary, probably the highlight of the afternoon.
Thhhaaat’s all for today, folks…
June 26, 2004
Delays
If the thunderstorms in Dallas do not totally disrupt my plans (looks like I’ve already missed my original flight to Charles de Gaulle), I should be in Paris sometime tomorrow morning. [Update (from DFW): Yup, missed that flight. My new flight gets into CDG at 11am.]
My agenda for the day involves
- Check into the