Resurgence in complex Chern-Simons theory at generic levels

Abstract

In this note we study the resurgent structure of $sl(2,\mathbb{C})$ Chern-Simons state integral models on knot complements $S^3\backslash 4_1,S^3\backslash 5_2$ with generic discrete level $k\ge 1$ 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 $k$.

46 pages, 6 figures, 7 tables, new references added

References in corpus (2)

• Generalized Volume Conjecture and the A-Polynomials -- the Neumann-Zagier Potential Function as a Classical Limit of Quantum Invariant
• Infrared phases of 3D Class R theories

Cited by in corpus (1)

• Resurgence in the Scalar Quantum Electrodynamics Euler-Heisenberg Lagrangian