2008/12/05 by Ori Ganor, Ganor, Ori J., Yoon Pyo Hong +1
Physics and Astronomy · Mathematics · #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.0812.1213
We propose a relation between the operator of S-duality (of N=4 super Yang-Mills theory in 3+1D) and a topological theory in one dimension lower. We construct the topological theory by compactifying N=4 super Yang-Mills on a circle with an S-duality and R-symmetry twist. The S-duality twist requires a selfdual coupling constant. We argue that for a sufficiently low rank of the gauge group the three-dimensional low-energy description is a topological theory, which we conjecture to be a pure Chern-Simons theory. This conjecture implies a connection between the action of mirror symmetry on the sigma-model with Hitchin's moduli space as target space and geometric quantization of the moduli space of flat connections on a Riemann surface.