Hecke modifications of Higgs bundles and the extended Bogomolny equation
Differential Geometry
2021-03-18 v2
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.
Keywords
Cite
@article{arxiv.1812.08994,
title = {Hecke modifications of Higgs bundles and the extended Bogomolny equation},
author = {Siqi He and Thomas Walpuski},
journal= {arXiv preprint arXiv:1812.08994},
year = {2021}
}
Comments
The singularity analysis in Section 11 builds on and extends arXiv:1610.08283