Warped AdS_5 Black Holes and Dual CFTs
Abstract
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.
Keywords
Cite
@article{arxiv.0901.2574,
title = {Warped AdS_5 Black Holes and Dual CFTs},
author = {Keiju Murata and Tatsuma Nishioka and Norihiro Tanahashi},
journal= {arXiv preprint arXiv:0901.2574},
year = {2009}
}
Comments
19 pages, 7 figures;