### Abstract

It is argued that the general four-dimensional extremal Kerr-Newman-AdS-dS black hole is holographically dual to a (chiral half of a) two-dimensional CFT, generalizing an argument given recently for the special case of extremal Kerr. Specifically, the asymptotic symmetries of the near-horizon region of the general extremal black hole are shown to be generated by a Virasoro algebra. Semiclassical formulae are derived for the central charge and temperature of the dual CFT as functions of the cosmological constant, Newton's constant and the black hole charges and spin. We then show, assuming the Cardy formula, that the microscopic entropy of the dual CFT precisely reproduces the macroscopic Bekenstein-Hawking area law. This CFT description becomes singular in the extreme Reissner-Nordstrom limit where the black hole has no spin. At this point a second dual CFT description is proposed in which the global part of the U(1) gauge symmetry is promoted to a Virasoro algebra. This second description is also found to reproduce the area law. Various further generalizations including higher dimensions are discussed.

Original language | English |
---|---|

Article number | 019 |

Journal | Journal of High Energy Physics |

Volume | 2009 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2009 |

Externally published | Yes |

### Fingerprint

### Keywords

- Black holes
- Black holes in string theory
- Space-time symmetries

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2009*(4), [019]. https://doi.org/10.1088/1126-6708/2009/04/019

**CFT duals for extreme black holes.** / Hartman, Thomas; Murata, Keiju; Nishioka, Tatsuma; Strominger, Andrew.

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, vol. 2009, no. 4, 019. https://doi.org/10.1088/1126-6708/2009/04/019

}

TY - JOUR

T1 - CFT duals for extreme black holes

AU - Hartman, Thomas

AU - Murata, Keiju

AU - Nishioka, Tatsuma

AU - Strominger, Andrew

PY - 2009

Y1 - 2009

N2 - It is argued that the general four-dimensional extremal Kerr-Newman-AdS-dS black hole is holographically dual to a (chiral half of a) two-dimensional CFT, generalizing an argument given recently for the special case of extremal Kerr. Specifically, the asymptotic symmetries of the near-horizon region of the general extremal black hole are shown to be generated by a Virasoro algebra. Semiclassical formulae are derived for the central charge and temperature of the dual CFT as functions of the cosmological constant, Newton's constant and the black hole charges and spin. We then show, assuming the Cardy formula, that the microscopic entropy of the dual CFT precisely reproduces the macroscopic Bekenstein-Hawking area law. This CFT description becomes singular in the extreme Reissner-Nordstrom limit where the black hole has no spin. At this point a second dual CFT description is proposed in which the global part of the U(1) gauge symmetry is promoted to a Virasoro algebra. This second description is also found to reproduce the area law. Various further generalizations including higher dimensions are discussed.

AB - It is argued that the general four-dimensional extremal Kerr-Newman-AdS-dS black hole is holographically dual to a (chiral half of a) two-dimensional CFT, generalizing an argument given recently for the special case of extremal Kerr. Specifically, the asymptotic symmetries of the near-horizon region of the general extremal black hole are shown to be generated by a Virasoro algebra. Semiclassical formulae are derived for the central charge and temperature of the dual CFT as functions of the cosmological constant, Newton's constant and the black hole charges and spin. We then show, assuming the Cardy formula, that the microscopic entropy of the dual CFT precisely reproduces the macroscopic Bekenstein-Hawking area law. This CFT description becomes singular in the extreme Reissner-Nordstrom limit where the black hole has no spin. At this point a second dual CFT description is proposed in which the global part of the U(1) gauge symmetry is promoted to a Virasoro algebra. This second description is also found to reproduce the area law. Various further generalizations including higher dimensions are discussed.

KW - Black holes

KW - Black holes in string theory

KW - Space-time symmetries

UR - http://www.scopus.com/inward/record.url?scp=67649516031&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67649516031&partnerID=8YFLogxK

U2 - 10.1088/1126-6708/2009/04/019

DO - 10.1088/1126-6708/2009/04/019

M3 - Article

AN - SCOPUS:67649516031

VL - 2009

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 4

M1 - 019

ER -