Resurgence in complex Chern-Simons theory

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.

56 pages, 19 figures. v2: references added

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• Walls of Marginal Stability and Dyon Spectrum in N=4 Supersymmetric String Theories
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• Quantum Knot Invariant for Torus Link and Modular Forms
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