Musings

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 $\mu=0$ a decade ago. Sen’s contribution was to generalize the formula to nonzero $\mu$.

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 $\mu=0$ — 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 ($Q_{1,0}=M$, $Q_{j,0}=0$ for $j\gt 0$). 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 $SU(3)$ 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 $S^3$) at $T_H= -1/(\log(7-4\sqrt{3})R$. 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.