Journal of High Energy Physics

, 2010:34 | Cite as

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



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.


M(atrix) Theories 1/N Expansion Confinement Gauge-gravity correspondence 


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Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  • Gautam Mandal
    • 1
  • Manavendra Mahato
    • 1
  • Takeshi Morita
    • 1
  1. 1.Department of Theoretical PhysicsTata Institute of Fundamental ResearchMumbaiIndia

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