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

Mandal, Gautam ; Mahato, Manavendra ; Morita, Takeshi (2010) Phases of one dimensional large N gauge theory in a 1/D expansion Journal of High Energy Physics, 2010 (2). Article ID 34. ISSN 1029-8479

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Official URL: http://link.springer.com/article/10.1007/JHEP02(20...

Related URL: http://dx.doi.org/10.1007/JHEP02(2010)034

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.

Item Type:Article
Source:Copyright of this article belongs to Springer-Verlag.
Keywords:M(atrix) Theories; 1/N Expansion; Confinement; Gauge-gravity Correspondence
ID Code:103570
Deposited On:26 Dec 2017 11:14
Last Modified:26 Dec 2017 11:14

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