Resurgence in complex Chern-Simons theory

2016/05/24 by Gukov, Sergei, Marino, Marcos, Putrov, Pavel · 3 citations
#FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Number Theory (math.NT) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1605.07615

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.

Cited by

• Quantum invariants of 3-manifolds and links: a review
• c_{\rm eff} from Resurgence at the Stokes Line
• c_eff from Surgery and Modularity

Related

• A resurgence analysis of the SU(2) Chern-Simons partition functions on a Brieskorn homology sphere Σ(2,5,7)
• Chern-Simons theory, analytic continuation and arithmetic
• Peacock patterns and resurgence in complex Chern-Simons theory
• Resurgence of Chern-Simons theory at the trivial flat connection
• c_{\rm eff} from Resurgence at the Stokes Line