### 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 |
---|---|

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

**Warped AdS5 black holes and dual CFTs.** / Murata, Keiju; Nlshloka, Tatsuma; Tanahashi, Norihiro.

Research output: Contribution to journal › Article

*Progress of Theoretical Physics*, vol. 121, no. 5, pp. 941-957. https://doi.org/10.1143/PTP.121.941

}

TY - JOUR

T1 - Warped AdS5 black holes and dual CFTs

AU - Murata, Keiju

AU - Nlshloka, Tatsuma

AU - Tanahashi, Norihiro

PY - 2009/5

Y1 - 2009/5

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=69549084992&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=69549084992&partnerID=8YFLogxK

U2 - 10.1143/PTP.121.941

DO - 10.1143/PTP.121.941

M3 - Article

AN - SCOPUS:69549084992

VL - 121

SP - 941

EP - 957

JO - Progress of Theoretical Physics

JF - Progress of Theoretical Physics

SN - 0033-068X

IS - 5

ER -