Abstract
We develop a Kobayashi–Hitchin-type correspondence between solutions of the extended Bogomolny equations on with Nahm pole singularity at and the Hitchin component of the stable Higgs bundle; this verifies a conjecture of Gaiotto and Witten. We also develop a partial Kobayashi–Hitchin correspondence for solutions with a knot singularity in this program, corresponding to the non-Hitchin components in the moduli space of stable Higgs bundles. We also prove existence and uniqueness of solutions with knot singularities on .
Citation
Siqi He. Rafe Mazzeo. "The extended Bogomolny equations and generalized Nahm pole boundary condition." Geom. Topol. 23 (5) 2475 - 2517, 2019. https://doi.org/10.2140/gt.2019.23.2475
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