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Reducing $S$- duality to $T$- duality
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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.
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Irregular KZ equations and Kac-Moody representations
Irregular Kac-Moody representations produce irregular KZ equations, and derivatives of irregular Liouville conformal blocks with screening charges satisfy these equations.
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