## Abstract

We study N = 4 super Yang-Mills theories on a three-sphere with two types of chemical potential. One is associated with the R-symmetry and the other with the rotational symmetry of S^{3} (SO(4) symmetry). These correspond to charged Kerr-AdS black holes via AdS/CFT. The exact partition functions at zero coupling are computed and the thermodynamical properties are studied. We find a nontrivial gap between the confinement/deconfinement transition line and the boundary of the phase diagram when we include more than four chemical potentials. In dual gravity, we find such a gap in the phase diagram by studying the thermodynamics of the charged Kerr-AdS black hole. This shows that the qualitative phase structures agree between both theories. We also find that the ratio between the thermodynamical quantities is close to well-known factor of 3/4 even at low temperatures.

Original language | English |
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Pages (from-to) | 473-508 |

Number of pages | 36 |

Journal | Progress of Theoretical Physics |

Volume | 120 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2008 Sept |

Externally published | Yes |

## ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)