Resurgence in complex Chern-Simons theory

TL;DR

This paper investigates the resurgence properties of the SU(2) Chern-Simons theory partition function on closed three-manifolds, revealing how contributions from different flat connections can be recovered from asymptotic expansions and exploring connections to various geometric and physical structures.

Contribution

It provides explicit analysis of resurgence in Chern-Simons theory, demonstrating how irreducible flat connections are encoded in asymptotic expansions around abelian connections, and explores related geometric connections.

Findings

Borel transforms have expected analytic properties in studied examples.

Contributions of irreducible flat connections can be recovered from abelian expansions.

Connections to Floer instanton moduli spaces and complex geodesics are discussed.

Abstract

We study resurgence properties of partition function of SU(2) Chern-Simons theory (WRT invariant) on closed three-manifolds. We check explicitly that in various examples Borel transforms of asymptotic expansions posses expected analytic properties. In examples that we study we observe that contribution of irreducible flat connections to the path integral can be recovered from asymptotic expansions around abelian flat connections. We also discuss connection to Floer instanton moduli spaces, disk instantons in 2d sigma models, and length spectra of "complex geodesics" on the A-polynomial curve.