A lower bound on the solutions of Kapustin-Witten equations

Abstract

In this article, we consider the Kapustin-Witten equations on a closed $4$-manifold. We study certain analytic properties of solutions to the equations on a closed manifold. The main result is that there exists an $L^2$-lower bound on the extra fields over a closed four-manifold satisfying certain conditions if the connections are not ASD connections. Furthermore, we also obtain a similar result about the Vafa-Witten equations.

Final version; to appear in Letters in Mathematical Physics. arXiv admin note: text overlap with arXiv:1409.1525, arXiv:1307.6447 by other authors

References in corpus (3)

• The zero loci of Z/2 harmonic spinors in dimension 2, 3 and 4
• Energy gap for Yang-Mills connections, I: Four-dimensional closed Riemannian manifolds
• On the singular sets of solutions to the Kapustin-Witten equations and the Vafa-Witten ones on compact Kähler surfaces

Cited by in corpus (5)

• Solutions of Kapustin-Witten equations for ADE-type groups
• An Energy Gap for Complex Yang-Mills Equations
• Inner Product in Highest-Weight Representation
• A compactness theorem for stable flat $SL(2,\mathbb{C})$ connections on $3$-folds
• On a topology property for the moduli space of Kapustin-Witten equations