2021/02/08 by Clifford Henry Taubes, Taubes, Clifford Henry
Mathematics · Physics and Astronomy · #53C07 #57R57 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2102.04290
openalex publication_date 2021/02/08 · openalex created_date 2021/02/15 · openalex updated_date 2026/07/28
A non-negative integer labeled set of model solutions to the ℝ-invariant Kapustin-Witten equations on (0,∞)× ℝ2× ℝ plays a central role in Edward Witten's program to interpret the colored Jones polynomial or a knot in the context of SU(2) gauge theory. This paper explains why there are ℝ-invariant solutions to these equations on (0,∞)× ℝ2× ℝ that interpolate between two model solutions as the (0,∞) parameter increases from 0 to ∞ while respecting the ℝ2 factor asymptotics. The only constraint on the limiting pair of model solutions is this: Letting m0 and m_∞ denote their non-negative integer labels, then m0 - m_∞ must be a positive, even integer. (As explained in the paper, there is a ℂ(m0 -m_∞ - 2)/2× ℂ^* moduli space of these interpolation solutions.)