  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.
