Resurgence in complex Chern-Simons theory at generic levels

TL;DR

This paper explores the resurgent structure of complex Chern-Simons theory at various levels, revealing universal features in the asymptotic series despite increasing complexity.

Contribution

It uncovers the universal resurgent structure of $sl(2, ext{C})$ Chern-Simons state integrals on knot complements at generic levels.

Findings

Resurgent structure is universal across levels.

Distribution of Borel plane singularities is level-independent.

Stokes constants are independent of the level.

Abstract

In this note we study the resurgent structure of $sl(2,\mathbb{C})$ Chern-Simons state integral models on knot complements $S^3\backslash\mathbf{4}_1,S^3\backslash\mathbf{5}_2$ with generic discrete level $k\geq 1$ and with small boundary holonomy deformation. The coefficients of the saddle point expansions are in the trace field of the knot extended by the holonomy parameter. Despite increasing complication of the asymptotic series as the level $k$ increases, the resurgent structure of the asymptotic series is universal: both the distribution of Borel plane singularities and the associated Stokes constants are independent of the level $k$.