Transmutation of a trans-series: the Gross-Witten-Wadia phase transition
Abstract
We study the change in the resurgent asymptotic properties of a trans-series in two parameters, a coupling g2 and a gauge index N, as a system passes through a large N phase transition, using the universal example of the Gross-Witten-Wadia third-order phase transition in the unitary matrix model. This transition is well-studied in the immediate vicinity of the transition point, where it is characterized by a double-scaling limit Painlevé II equation, and also away from the transition point using the pre-string difference equation. Here we present a complementary analysis of the transition at all coupling and all finite N, in terms of a differential equation, using the explicit Tracy-Widom mapping of the Gross-Witten-Wadia partition function to a solution of a Painlevé III equation. This mapping provides a simple method to generate trans-series expansions in all parameter regimes, and to study their transmutation as the parameters are varied. For example, at any finite N the weak coupling expansion is divergent, with a non-perturbative trans-series completion; on the other hand, the strong coupling expansion is convergent, and yet there is still a non-perturbative trans-series completion. We show how the different instanton terms ‘condense’ at the transition point to match with the double-scalingmore »
- Authors:
-
- Univ. of Connecticut, Storrs, CT (United States)
- Publication Date:
- Research Org.:
- Univ. of Connecticut, Storrs, CT (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP)
- OSTI Identifier:
- 1501886
- Grant/Contract Number:
- SC0010339
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of High Energy Physics (Online)
- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 11; Journal ID: ISSN 1029-8479
- Publisher:
- Springer Berlin
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 97 MATHEMATICS AND COMPUTING; Nonperturbative Effects; 1/N Expansion; Matrix Models
Citation Formats
Ahmed, Anees, and Dunne, Gerald V. Transmutation of a trans-series: the Gross-Witten-Wadia phase transition. United States: N. p., 2017.
Web. doi:10.1007/jhep11(2017)054.
Ahmed, Anees, & Dunne, Gerald V. Transmutation of a trans-series: the Gross-Witten-Wadia phase transition. United States. doi:10.1007/jhep11(2017)054.
Ahmed, Anees, and Dunne, Gerald V. Thu .
"Transmutation of a trans-series: the Gross-Witten-Wadia phase transition". United States. doi:10.1007/jhep11(2017)054. https://www.osti.gov/servlets/purl/1501886.
@article{osti_1501886,
title = {Transmutation of a trans-series: the Gross-Witten-Wadia phase transition},
author = {Ahmed, Anees and Dunne, Gerald V.},
abstractNote = {We study the change in the resurgent asymptotic properties of a trans-series in two parameters, a coupling g2 and a gauge index N, as a system passes through a large N phase transition, using the universal example of the Gross-Witten-Wadia third-order phase transition in the unitary matrix model. This transition is well-studied in the immediate vicinity of the transition point, where it is characterized by a double-scaling limit Painlevé II equation, and also away from the transition point using the pre-string difference equation. Here we present a complementary analysis of the transition at all coupling and all finite N, in terms of a differential equation, using the explicit Tracy-Widom mapping of the Gross-Witten-Wadia partition function to a solution of a Painlevé III equation. This mapping provides a simple method to generate trans-series expansions in all parameter regimes, and to study their transmutation as the parameters are varied. For example, at any finite N the weak coupling expansion is divergent, with a non-perturbative trans-series completion; on the other hand, the strong coupling expansion is convergent, and yet there is still a non-perturbative trans-series completion. We show how the different instanton terms ‘condense’ at the transition point to match with the double-scaling limit trans-series. Furthermore, we also define a uniform large N strong-coupling expansion (a non-linear analogue of uniform WKB), which is much more precise than the conventional large N expansion through the transition region, and apply it to the evaluation of Wilson loops.},
doi = {10.1007/jhep11(2017)054},
journal = {Journal of High Energy Physics (Online)},
number = 11,
volume = 2017,
place = {United States},
year = {2017},
month = {11}
}
Web of Science
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