English

Resurgence in complex Chern-Simons theory

High Energy Physics - Theory 2016-10-24 v2 Mathematical Physics Geometric Topology math.MP Number Theory Quantum Algebra

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.

Keywords

Cite

@article{arxiv.1605.07615,
  title  = {Resurgence in complex Chern-Simons theory},
  author = {Sergei Gukov and Marcos Marino and Pavel Putrov},
  journal= {arXiv preprint arXiv:1605.07615},
  year   = {2016}
}

Comments

56 pages, 19 figures. v2: references added

R2 v1 2026-06-22T14:08:39.266Z