Non-Perturbative Large N Trans-series for the Gross-Witten-Wadia Beta Function

TL;DR

This paper analyzes the non-perturbative trans-series structure of the large N beta function in the Gross-Witten-Wadia matrix model, revealing how it evolves across the phase transition and providing a comprehensive understanding of the model's running coupling.

Contribution

It introduces the non-perturbative trans-series for the beta function at both weak and strong coupling in the large N limit, detailing how the structure changes across the phase transition.

Findings

Trans-series structure varies across the phase transition.

Perturbative beta function gains non-perturbative completion at finite N.

Analysis applies to the running coupling in the matrix model.

Abstract

We describe the non-perturbative trans-series, at both weak- and strong-coupling, of the large N approximation to the beta function of the Gross-Witten-Wadia unitary matrix model. This system models a running coupling, and the structure of the trans-series changes as one crosses the large N phase transition. The perturbative beta function acquires a non-perturbative trans-series completion at large but finite $N$ in the 't Hooft limit, as does the running coupling.