## Abstract

Solutions of type IIB supergravity which preserve half of the supersymmetries have a dual description in terms of free fermions, as elucidated by the ''bubbling AdS" construction of Lin, Lunin and Maldacena. In this paper we study the half-BPS geometry associated with a gas of free fermions in thermodynamic equilibrium obeying the Fermi-Dirac distribution. We consider both regimes of low and high temperature. In the former case, we present a detailed computation of the ADM mass of the supergravity solution and find agreement with the thermal energy of the fermions. The solution has a naked null singularity and, by general arguments, is expected to develop a finite area horizon once stringy corrections are included. By introducing a stretched horizon, we propose a way to match the entropy of the fermions with the entropy of the geometry in the low temperature regime. In the opposite limit of high temperature, the solution resembles a dilute gas of D3 branes. Also in this case the ADM mass of the geometry agrees with the thermal energy of the fermions.

Original language | English (US) |
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Article number | 067 |

Journal | Journal of High Energy Physics |

Volume | 2007 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2007 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

## Keywords

- AdS-CFT correspondence
- Black holes in string theory
- Supergravity models