Resurgence and topological strings

摘要

The mathematical idea of resurgence allows one to obtain non-perturbative information from the large-order behavior of perturbative expansions. This idea can be very fruitful in physics applications, in particular if one does not have access to such nonperturbative information from first principles. An important example is topological string theory, which is a priori only defined as an asymptotic perturbative expansion in the coupling constant gs. We show how the idea of resurgence can be combined with the holomorphic anomaly equation to extend the pert urbative definition of the topological string and obtain, in a model-independent way, a large amount of information about its nonpert urbative structure.