Sequences of Nahm pole solutions to the SU(2) Kapustin-Witten equations

Abstract

This paper describes the behavior of sequences of solutions to the Kapustin-Witten equations with Nahm pole asymptotics on the product of the half-line with a compact, oriented, Riemannian 3-manifold. These sequences have sub-sequences that either converge to another solution after acting term-wise by an automorphism of the principle bundle, or they converge after renormalization to a (weak) Z/2 harmonic 1-form from the 3-manifold; it is independent of the half-line coordinate in the product structure.

Some typos corrected and some arguments simplified in this version

References in corpus (2)

• The zero loci of Z/2 harmonic spinors in dimension 2, 3 and 4
• Energy bound for Kapustin-Witten solutions on $S^3\times {\mathbb{R}}^{+}$

Cited by in corpus (5)

• Invariants of 4-manifolds from Khovanov-Rozansky link homology
• Classification of Nahm pole solutions of the Kapustin-Witten equations on $S^1\times \Sigma \times {\mathbb{R}}^{+}$
• The Expansions of the Nahm Pole Solutions to the Kapustin-Witten Equations
• Opers and the twisted Bogomolny equations
• Lectures on the linearized Kapustin-Witten equations on $(0,\infty )\times$Y