Reducing $S$- duality to $T$- duality

TL;DR

The paper demonstrates that in N=4 Yang-Mills theory compactified on a torus, S-duality predictions can be derived from T-duality of an associated conformal field theory, reducing a four-dimensional duality to a two-dimensional one.

Contribution

It shows that S-duality in four-dimensional Yang-Mills theory can be understood through T-duality in an effective two-dimensional conformal field theory, simplifying the duality relationship.

Findings

S-duality predictions follow from T-duality in the effective CFT

Montonen-Olive duality reduces to momentum-winding duality

Effective theory is conjectured to be an orbifold involving the maximal torus of G

Abstract

The infrared limit of $D=4,~~N=4$ Yang-Mills theory with compact gauge group $G$ compactified on a two-torus is governed by an effective superconformal field theory. We conjecture that this is a certain orbifold involving the maximal torus of $G$. Yang-Mills $S$-duality makes predictions for all correlators of this effective conformal field theory. These predictions are shown to be implied by the standard $T$-duality of the conformal field theory. Consequently, Montonen-Olive duality between electric and magnetic states reduces to the standard two-dimensional duality between momentum and winding states.