## 抄録

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.

本文言語 | English |
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ページ（範囲） | 941-957 |

ページ数 | 17 |

ジャーナル | Progress of Theoretical Physics |

巻 | 121 |

号 | 5 |

DOI | |

出版ステータス | Published - 2009 5 |

## ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)