A lower bound on the solutions of Kapustin-Witten equations
arXiv:1601.07986 · doi:10.1007/s11005-016-0910-2
Abstract
In this article, we consider the Kapustin-Witten equations on a closed -manifold. We study certain analytic properties of solutions to the equations on a closed manifold. The main result is that there exists an -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.
arXiv commentFinal 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 (14)
- A Strong Coupling Test of S-Duality
- Analytic Continuation Of Chern-Simons Theory
- Knot Invariants from Four-Dimensional Gauge Theory
- Fukaya-Seidel category and gauge theory
- Global existence and convergence of solutions to gradient systems and applications to Yang-Mills gradient flow
- PSL(2;C) connections on 3-manifolds with L2 bounds on curvature
- PU(2) Monopoles, I: Regularity, Uhlenbeck Compactness, and Transversality
- 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
- Donaldson invariants and wall-crossing formulas. I: Continuity of gluing maps
- Some boundedness properties of solutions to the Vafa-Witten equations on closed four-manifolds
- Geometric aspects of the Kapustin-Witten equations
- On the singular sets of solutions to the Kapustin-Witten equations and the Vafa-Witten ones on compact Kähler surfaces
- Compactness theorems for SL(2;C) generalizations of the 4-dimensional anti-self dual equations