### 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.

Original language | English |
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Pages (from-to) | 941-957 |

Number of pages | 17 |

Journal | Progress of Theoretical Physics |

Volume | 121 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2009 May |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Cite this

*Progress of Theoretical Physics*,

*121*(5), 941-957. https://doi.org/10.1143/PTP.121.941