Classification of Nahm pole solutions of the Kapustin-Witten equations on $S^1\times \Sigma \times {\mathbb{R}}^{+}$

Abstract

In this note, we classify all solutions to the $\mathrm{SU}(\mathrm{n})$ Kapustin-Witten equations on $S^1\times \Sigma \times {\mathbb{R}}^{+}$, where $\Sigma$ is a compact Riemann surface, with Nahm pole singularity at $S^1\times \Sigma \times \{0\}$. We provide a similar classification of solutions with generalized Nahm pole singularities along a simple divisor (a "knot") in $S^1\times \Sigma \times \{0\}$.

14 pages

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