Reducing S duality to T duality

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, the Montonen-Olive duality between electric and magnetic states reduces to the standard two-dimensional duality between momentum and winding states.