The Resurgence of Instantons in String Theory

By Inês Aniceto, R. Schiappa, M. Vonk. 2011

165 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/1d86689ea18f03e2a3f407bdd338945ef4e3cbe6

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Citations in the corpus

Resurgence theory, ghost-instantons, and analytic continuation of path integrals (2013, unknown): “• In matrix model/string perturbation theories, it seems plausible that the terms in the trans-series exhibiting exponential growth [17, 18] may be associated with some D-brane analogs of the ghost-instantons in QM;13 see also [16].”
Lectures on non‐perturbative effects in large N gauge theories, matrix models and strings (2012, background): “134) one finds the loop expansion of the one-instanton free energy, see [94, 10] for explicit formulae.”
The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects (2012, methodology): “We note that similar expressions have appeared in the context of matrix models and topological string theory [38, 67] and by using the bridge equations in the context of resurgence theory in [39].”
A primer on resurgent transseries and their asymptotics (2018, methodology): “One can also write general closed-form formulae, for all these quantities, based on sums over partitions, but we refer the interested reader to section 2 of [16] for those.”
Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles (2014, background): “3.1 Perturbation theory on R2 and IR-renormalons 22”
An introduction to resurgence, trans-series and alien calculus (2014, background): “ly the case when the problem at hand depends on just one single boundary condition. It is possible to obtain theories where one has multiple instantonic congurations with dierent actions S a;S b;:::[41], and even complex valued action for the so called ghost-instantons [42] or more generically non-t”