Ricardo Couso Santamaria, Santiago de Compostela
Resurgence and the Topological String

Topological string theory is simple enough to be solved perturbatively, yet it is able to compute amplitudes in string theory and it also enjoys large N dualities. These gauge theory duals, sometimes in the form of matrix models, can be solved past perturbation theory by plugging transseries ansätze into the so-called string equation. Based on the mathematics of resurgence, developed in the 80's by J. Ecalle, this approach has been recently applied with tremendous success to matrix models and their double-scaling limits (Painlevé I, etc). A natural question is if something similar can be done in the stringy side. In this seminar I will show how the holomorphic anomaly equations of Bershadsky-Cecotti-Ooguri-Vafa (BCOV) provide the starting point to derive a master equation which can be solved with a transseries ansatz. I will review the perturbative sector of the solutions, its structure and how it generalizes for higher instanton sectors. Some resurgence in the guise of large-order behavior of the perturbative sector will be used to derive the holomorphicity of the instanton actions that control the asymptotics of the perturbative sector. This work will appear shortly in a paper together with J.D. Edelstein, R. Schiappa and M. Vonk.