Peculiar properties of a charged dilatonic black hole in AdS_5

TL;DR

This paper analyzes a charged dilatonic black hole in AdS_5 with properties resembling a Fermi liquid, including entropy proportional to temperature and normal modes for bulk fermions, suggesting a potential duality.

Contribution

It introduces an analytically tractable charged dilatonic black hole in AdS_5 with properties indicative of Fermi liquid behavior, embedded in string theory.

Findings

Entropy proportional to temperature at low T

Supports normal modes of massless, charged fermions

Exhibits thermodynamic instability at low temperatures

Abstract

We study a charged dilatonic black hole in AdS_5, 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 AdS_3 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.