Title: 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 g ² 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 themore » 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.« less

Authors:

Ahmed, Anees ^[1]; Dunne, Gerald V. ^[1]

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1. Univ. of Connecticut, Storrs, CT (United States)

Publication Date:

2017-11-09

Research Org.:

Univ. of Connecticut, Storrs, CT (United States)

Sponsoring Org.:

USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

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