The Resurgence of Instantons in String Theory

TL;DR

This paper explores nonperturbative effects in string theory using transseries and resurgent analysis, revealing new sectors beyond D-branes necessary for a complete nonperturbative understanding.

Contribution

It introduces a detailed application of transseries and resurgent analysis to string theory, extending the understanding of nonperturbative sectors beyond D-branes.

Findings

Nonperturbative solutions relate to large-order perturbation behavior.

Resurgent analysis applies to topological strings and matrix models.

Additional nonperturbative sectors are needed beyond D-branes.

Abstract

Nonperturbative effects in string theory are usually associated to D-branes. In many cases it can be explicitly shown that D-brane instantons control the large-order behavior of string perturbation theory, leading to the well-known (2g)! growth of the genus expansion. This paper presents a detailed treatment of nonperturbative solutions in string theory, and their relation to the large-order behavior of perturbation theory, making use of transseries and resurgent analysis. These are powerful techniques addressing general nonperturbative contributions within non-linear systems, which are developed at length herein as they apply to string theory. The cases of topological strings, the Painleve I equation describing 2d quantum gravity, and the quartic matrix model, are explicitly addressed. These results generalize to minimal strings and general matrix models. It is shown that, in order to completely understand string theory at a fully nonperturbative level, new sectors are required beyond the standard D-brane sector.