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From S-Duality to Chern-Simons via Minimal StringsQMAP Seminar
|Speaker: ||Ori Ganor, Berkeley|
|Location: ||2112 MSB|
|Start time: ||Thu, Apr 30 2009, 3:10PM|
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.