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arXiv · 0910.4526

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

Gautam Mandal·Manavendra Mahato·Takeshi Morita
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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.

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Gautam Mandal, Manavendra Mahato, Takeshi Morita. 2010-02-03. Phases of one dimensional large N gauge theory in a 1/D expansion. https://doi.org/10.1007/jhep02(2010)034

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