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The resurgence of instantons in string theory

The resurgence of instantons in string theory
The resurgence of instantons in string theory
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.
hep-th, cond-mat.stat-mech, math-ph, math.MP, nlin.SI
1931-4523
339-496
Aniceto, Inês
0061ca0c-1ad8-4510-9b12-008e5c27a7ea
Schiappa, Ricardo
7b7a5b7d-7ecc-454e-ba14-51c2adc24c5f
Vonk, Marcel
510bcb5c-8379-4fce-af57-83b41843e02c
Aniceto, Inês
0061ca0c-1ad8-4510-9b12-008e5c27a7ea
Schiappa, Ricardo
7b7a5b7d-7ecc-454e-ba14-51c2adc24c5f
Vonk, Marcel
510bcb5c-8379-4fce-af57-83b41843e02c

Aniceto, Inês, Schiappa, Ricardo and Vonk, Marcel (2012) The resurgence of instantons in string theory. Communications in Number Theory and Physics, 6 (2), 339-496. (doi:10.4310/CNTP.2012.v6.n2.a3).

Record type: Article

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.

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More information

e-pub ahead of print date: 19 October 2012
Published date: 2012
Additional Information: 108 pages; v2,v3: references added; v4: improved pedagogical content, final version for CNTP; v5: typos corrected
Keywords: hep-th, cond-mat.stat-mech, math-ph, math.MP, nlin.SI

Identifiers

Local EPrints ID: 424144
URI: https://eprints.soton.ac.uk/id/eprint/424144
ISSN: 1931-4523
PURE UUID: ca9c1328-35cc-476e-8825-60d02928fa94

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Date deposited: 05 Oct 2018 11:30
Last modified: 01 Nov 2018 17:30

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