The algebra of Wilson–'t Hooft operators

Abstract

We study the Operator Product Expansion of Wilson–'t Hooft operators in a twisted N = 4 super-Yang–Mills theory with gauge group G. The Montonen–Olive duality puts strong constraints on the OPE and in the case G = SU ( 2 ) completely determines it. From the mathematical point of view, the Montonen–Olive duality predicts the L 2 Dolbeault cohomology of certain equivariant vector bundles on Schubert cells in the affine Grassmannian. We verify some of these predictions. We also make some general observations about higher categories and defects in Topological Field Theories.