Phases of one dimensional large N gauge theory in a 1/D expansion

TL;DR

This paper analyzes large N Yang Mills theory with many adjoint scalars in low dimensions, revealing phase transitions related to confinement and deconfinement, using a 1/D expansion and connecting to Gregory-Laflamme transitions.

Contribution

It introduces a 1/D expansion approach to study phase structure in large N gauge theories with adjoint scalars, identifying transitions analogous to confinement and Gregory-Laflamme.

Findings

Existence of a non-trivial saddle point with a mass gap.

Identification of a second order transition from uniform to non-uniform eigenvalue distribution.

Observation of a Gross-Witten-Wadia transition with eigenvalue gap formation.

Abstract

We consider large N Yang Mills theory with D adjoint scalar fields in d dimensions for d=0 or 1. We show the existence of a non-trivial saddle point of the functional integral at large D which is characterized by a mass gap for the adjoint scalars. We integrate out the adjoint scalars in a 1/D expansion around the saddle point. In case of one dimension which is regarded as a circle, this procedure leads to an effective action for the Wilson line. We find an analogue of the confinement/deconfinement transition which consists of a second order phase transition from a uniform to a non-uniform eigenvalue distribution of the Wilson line, closely followed by a Gross-Witten-Wadia transition where a gap develops in the eigenvalue distribution. The phase transition can be regarded as a continuation of a Gregory-Laflamme transition. Our methods involve large values of the dimensionless 'tHooft coupling. The analysis in this paper is quantitatively supported by earlier numerical work for D=9.