### Abstract

We study a charged dilatonic black hole in AdS5, derived from a Lagrangian involving a gauge field whose kinetic term is modified by the exponential of a neutral scalar. This black hole has two properties which one might reasonably demand of the dual of a Fermi liquid: Its entropy is proportional to temperature at low temperature, and its extremal limit supports normal modes of massless, charged bulk fermions. The black hole we study has a simple analytic form because it can be embedded in type IIB string theory as the near-horizon limit of D3-branes with equal spins in two of the three independent transverse planes. Two further properties can be deduced from this embedding: There is a thermodynamic instability, reminiscent of ferromagnetism, at low temperatures; and there is an AdS3 factor in the extremal near-horizon geometry which accounts for the linear dependence of entropy on temperature. Altogether, it is plausible that the dilatonic black hole we study, or a relative of it with similar behavior in the infrared, is the dual of a Fermi liquid; however, the particular embedding in string theory that we consider is unlikely to have such a dual description, unless through some unexpected boson-fermion equivalence at large N.

Original language | English (US) |
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Article number | 046001 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 81 |

Issue number | 4 |

DOIs | |

State | Published - Feb 1 2010 |

### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)

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## Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*81*(4), [046001]. https://doi.org/10.1103/PhysRevD.81.046001