Schedule Mar 19, 2009
From S-Duality to Chern-Simons via Minimal Strings
Ori Ganor, UC Berkeley

There are two special values of the coupling constant for which there exist noncentral elements of SL(2,Z) that map N=4 Super Yang-Mills theory with gauge group U(n) to itself. At these values, the field theory can be compactified on a circle with duality-twisted boundary conditions. The low-energy limit of this model directly probes the S-duality operator. Augmented by an R-symmetry twist, and with additional restrictions on the rank n, this low-energy limit appears to be a nontrivial topological field theory. Upon further compactification on a torus, the Hilbert space of the low-energy theory can be mapped, using U-duality, to the finite dimensional space of minimal string states on a three-dimensional manifold that is a torus fibre-bundle over a circle. Using the string theory realization, I'll compare the low-energy theory with Chern-Simons theory. Also, compactification on a Riemann surface of higher genus suggests a relation between the dimension of the Hilbert space of certain Chern-Simons theories on the Riemann surface and the supertrace of the action induced by mirror symmetry on the appropriate cohomology of the appropriate Hitchin space.

Other video options

To begin viewing slides, click on the first slide below. (Or, view as pdf.)


[01] [02] [03] [04] [05] [06] [07] [08] [09] [10]

Author entry (protected)