Abstract

Building on recent progress in the study of the enumerative invariants of theories based on quantum curves within the analytic framework of resurgence, I will discuss how the machinery of resurgence can be applied to the asymptotic series that arise naturally as perturbative expansions in a strongly-coupled limit of topological string theory on a toric Calabi-Yau threefold. These asymptotic series show infinite towers of singularities in their Borel plane. The corresponding infinitely-many Stokes constants can be regarded as a new conjectural class of topological invariants of the underlying theory, and they can be organized as coefficients of generating functions given by q-series. I will present an explicit analysis of a well-known example of toric Calabi-Yau geometry, whose resurgent structure turns out to be analytically solvable. This leads to proven exact formulae for the Stokes constants in the strong coupling regime. The analytic approach that I propose is then straightforwardly extended to the dual weakly-coupled limit of topological strings on the same background, which has been studied numerically in a recent work by Gu and Mariño.