Warped AdS_5 Black Holes and Dual CFTs

Details Warped AdS_5 Black Holes and Dual CFTs Warped AdS_5 Black Holes and Dual CFTs

2009-01-19

arxiv.org/abs/0901.2574v4

Prog.Theor.Phys.121:941-957,2009

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, 7 figures;

Scientific paper

10.1143/PTP.121.941

We consider a black hole solution whose spatial boundary is a squashed three sphere in Einstein gravity with negative cosmological constant. We solve the Einstein equations numerically and find a warped AdS black hole solution with arbitrary squashing parameter. This solution becomes the ordinary AdS-Schwarzschild solution when the squashing parameter is chosen appropriately. Motivated by this fact, we study N=4 super Yang-Mills theory with zero coupling constant on a squashed three sphere and show that the thermodynamical entropy of this theory roughly agrees with that of the warped AdS black hole up to a factor of 3/4. We also study the confinement/deconfinement transition of the gauge theory. We evaluate the approximate Hawking-Page transition temperature of the warped AdS black hole and find a qualitative agreement between the transition temperatures of the gravity and the gauge theory. These results suggest a duality between the warped AdS solution and N=4 super Yang-Mills theory on a squashed three sphere.

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