The Resurgent Structure of Topological Strings

Explore the resurgent structure of topological strings in this 58-minute lecture by Marcos Mariño from the Université de Genève. Delve into the perturbation theory of topological strings, described by factorially divergent series, and examine their Borel singularities and alien derivatives. Learn about trans-series solutions of the holomorphic anomaly equations of BCOV and discover exact formulae for relevant trans-series. Investigate a general conjecture for the resurgent structure of topological string theory, tested in compact and non-compact Calabi-Yau manifolds and matrix models. Compare the resulting structure with similar results on quantum periods and understand the complexity of Stokes automorphisms in topological string theory beyond the Delabaere-Pham formula. Gain insights into the ongoing search for a non-perturbative understanding of topological string theory and explore experimental evidence from the quintic Calabi-Yau manifold.

Intro
The search for a non-perturbative understanding of (topological) string theory has been going on for many years.
The resurgent structure associated to a formal power series is the set of all its alien derivatives at all its singularities (i.e. trans-series plus Stokes constants)
manifold M one can calculate periods by integrating the holomorphic 3-form over a symplectic basis of 3-cycles
String perturbation theory tells us that the total free energy is a formal power series involving a small parameter, a.k.a. the string coupling constant, and we have to sum over all genera
In this formulation, S is essentially an arbitrary variable. The conventional topological string free energies are recovered in the so-called holomorphic limit, where S becomes a (known) function of z.
Experimental evidence: asymptotics in the quintic CY