Communications in Number Theory and Physics

Volume 6 (2012)

Number 2

The resurgence of instantons in string theory

Pages: 339 – 496

DOI: http://dx.doi.org/10.4310/CNTP.2012.v6.n2.a3

Authors

Inês Aniceto (Departamento de Matemática, Instituto Superior Técnico, Lisboa, Portugal)

Ricardo Schiappa (Departamento de Matemática, Instituto Superior Técnico, Lisboa, Portugal)

Marcel Vonk (Departamento de Matemática, Instituto Superior Técnico, Lisboa, Portugal)

Abstract

Nonperturbative effects in string theory are usuallyassociated to D-branes. In many cases it can be explicitlyshown that D-brane instantons control the large-orderbehavior of string perturbation theory, leading to thewell-known $(2g)!$ growth of the genus expansion.This paper presents a detailed treatment of nonperturbative\hbox{solutions} in string theory, and their relation tothe\break large-order behavior of perturbation theory,making use of trans-series and resurgent analysis.These are powerful techniques addressing generalnonperturbative contributions within non–linear systems,which are developed at length herein as they apply tostring theory. The cases of topological strings, thePainlevé I equation describing 2d quantum gravity, andthe quartic matrix model, are explicitly addressed. Theseresults generalize to minimal strings and general matrixmodels. It is shown that, in order to completely understandstring theory at a fully nonperturbative level, new sectorsare required beyond the standard D-brane sector.

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