Free Fermions and Thermal AdS/CFT

Abstract

The dynamics of finite temperature U(N) gauge theories on $S^3$ 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 $\mathrm{Tr}U$. 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.

(0+34) pages and 9 figures, v2 references added

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Cited by in corpus (26)

• Black Holes as Effective Geometries
• Diagonal free field matrix correlators, global symmetries and giant gravitons
• String Theory as a Higher Spin Theory
• A double coset ansatz for integrability in AdS/CFT
• Spin Matrix Theory: A quantum mechanical model of the AdS/CFT correspondence
• N=4 SYM on S^3 with Near Critical Chemical Potentials
• Exact Stringy Microstates from Gauge Theories
• Warped AdS_5 Black Holes and Dual CFTs
• Monte Carlo Studies of the GWW Phase Transition in Large-N Gauge Theories
• Microstates of a $2d$ Black Hole in string theory
• Hedgehog black holes and the Polyakov loop at strong coupling
• Chern-Simons Theory on Seifert Manifold and Matrix Model
• The growth of the $\frac{1}{16}$-BPS index in 4d $\mathcal{N}=4$ SYM
• Emergent Phase Space Description of Unitary Matrix Model
• From Hagedorn to Lee-Yang: Partition functions of $\mathcal{N}=4$ SYM theory at finite $N$
• Phase Transitions of Charged Kerr-AdS Black Holes from Large-N Gauge Theories
• From Phase Space to Integrable Representations and Level-Rank Duality
• Phase Space Distribution for Two-Gap Solution in Unitary Matrix Model
• Phase Space Distribution of Riemann Zeros
• Kazakov-Migdal model on the Graph and Ihara Zeta Function
• Interior analysis, stretched technique and bubbling geometries
• The Giant Graviton Expansion
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• Phase Structure of Beta-deformed N=4 SYM on S^3 with Chemical Potentials
• Quantum Mechanics of Plancherel Growth
• A Unitary Matrix Model for $q$-deformed Plancherel Growth