Selfduality and Chern-Simons Theory

Abstract

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.

60 pages, references added

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Cited by in corpus (6)

• S-folds and 4d N=3 superconformal field theories
• Non-Invertible Symmetries of $\mathcal{N}=4$ SYM and Twisted Compactification
• Index theorem for topological excitations on R^3 * S^1 and Chern-Simons theory
• Holographic duals of 3d S-fold CFTs
• Static Charges in the Low-Energy Theory of the S-Duality Twist
• Ground States of Duality-twisted Sigma-Models with K3 Target Space