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

2018/08/12 by Siqi He, He, Siqi
Mathematics · #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1808.03886

openalex publication_date 2018/08/12 · openalex created_date 2018/08/22 · openalex updated_date 2026/07/28

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× (0,+∞). Let y be the coordinate of (0,+∞), we prove that the sub-leading terms of a polyhomogeneous Nahm pole solution is smooth to the boundary when y→ 0 if and only if X is an Einstein 3-manifold.

Citations

• Energy bound for Kapustin-Witten solutions on S³×ℝ⁺
• Sequences of Nahm pole solutions to the SU(2) Kapustin-Witten equations

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