The algebra of Wilson-'t Hooft operators
Anton Kapustin, Natalia Saulina
TL;DR
This paper investigates the operator product expansion of Wilson-'t Hooft operators in twisted N=4 super-Yang-Mills theory, exploring duality constraints and mathematical structures like equivariant cohomology and affine Grassmannians.
Contribution
It provides a detailed analysis of the OPE of Wilson-'t Hooft operators under duality constraints and verifies mathematical predictions related to equivariant vector bundles and cohomology.
Findings
Duality constrains the OPE in G=SU(2) case
Verification of Dolbeault cohomology predictions
Insights into higher categories and defects in TFTs
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.
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