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Hecke modifications of Higgs bundles and the extended Bogomolny equation

Published 21 Dec 2018 in math.DG | (1812.08994v2)

Abstract: We establish a Kobayashi-Hitchin correspondence between solutions of the extended Bogomolny equation with a Dirac type singularity and Hecke modifications of Higgs bundles. This correspondence was conjectured by Witten and plays an important role in the physical description of the the geometric Langlands program in terms of S-duality for N=4 super Yang-Mills theory in four dimensions.

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