Warped AdS_5 Black Holes and Dual CFTs

TL;DR

This paper explores a new warped AdS_5 black hole solution with a squashed boundary sphere, investigates its thermodynamics, and suggests a duality with N=4 super Yang-Mills theory on a squashed three sphere, showing qualitative agreement in entropy and phase transition temperatures.

Contribution

It introduces a numerically found warped AdS black hole with arbitrary squashing and connects it to the thermodynamics and phase transitions of N=4 super Yang-Mills theory on a squashed sphere.

Findings

Warped AdS black hole solutions depend on squashing parameter.

Thermodynamical entropy roughly matches gauge theory predictions.

Qualitative agreement in confinement/deconfinement transition temperatures.

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.