2007/11/10 by Suvankar Dutta, Rajesh Gopakumar
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #hep-th
paper · pdf · doi:10.1088/1126-6708/2008/03/011
published as JHEP0803:011,2008 · (0+34) pages and 9 figures, v2 references added
arxiv created 2007/11/10 · openalex publication_date 2008/03/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The dynamics of finite temperature U(N) gauge theories on S3 can be described, at weak coupling, by an effective unitary matrix model. Here we present an exact solution to these models, for any value of N, in terms of a sum over representations. Taking the large N limit of this solution provides a new perspective on the deconfinement transition which is supposed to be dual to the Hawking-Page transition. The large N phase transition manifests itself here in a manner similar to the Douglas-Kazakov phase transition in 2d Yang-Mills theory. We carry out a complete analysis of the saddle representation in the simplest case involving only the order parameter \rm TrU. We find that the saddle points corresponding to thermal AdS, the small black hole and the large black hole can all be described in terms of free fermions. They all admit a simple phase space description \it a la the BPS geometries of Lin, Lunin and Maldacena.