Resurgent Transseries and the Holomorphic Anomaly: Nonperturbative Closed Strings in Local CP2

Understand

The holomorphic anomaly equations describe B-model closed topological strings in Calabi-Yau geometries.

• Having been used to construct perturbative expansions, it was recently shown that they can also be extended past perturbation theory by making use of resurgent transseries.
• These yield formal nonperturbative solutions, showing integrability of the holomorphic anomaly equations at the nonperturbative level.
• This paper takes such constructions one step further by working out in great detail the specific example of topological strings in the mirror of the local CP2 toric Calabi-Yau background, and by addressing the associated (resurgent) large-order analysis of both perturbative and multi-instanton sectors.