The Expansions of the Nahm Pole Solutions to the Kapustin-Witten Equations

Abstract

For a 3-manifold $X$ and compact simple Lie group $G$, we study the expansions of polyhomogeneous Nahm pole solutions to the Kapustin-Witten equations over $X\times (0,+\infty )$. Let $y$ be the coordinate of $(0,+\infty )$, we prove that the sub-leading terms of a polyhomogeneous Nahm pole solution is smooth to the boundary when $y\to 0$ if and only if $X$ is an Einstein 3-manifold.

19 pages

References in corpus (3)

• Teichmuller TQFT vs Chern-Simons Theory
• Sequences of Nahm pole solutions to the SU(2) Kapustin-Witten equations
• Energy bound for Kapustin-Witten solutions on $S^3\times {\mathbb{R}}^{+}$

Cited by in corpus (1)

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