Peculiar properties of a charged dilatonic black hole inAdS5

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 nearhorizon 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 .

Fermi surfaces and gauge-gravity duality

“…The challenge for the future is to describe the phases of Sections V and VI using the dual gravity theory, in a manner which captures their expected properties of finite-range models in d = 2 and d = 3 respectively, and there have been recent studies in this direction [10,[12][13][14][15][16][17][18]20]. In particular, the d = 3 model of Gubser and Rocha [10] is a promising model for future study.…”

“…In particular, the d = 3 model of Gubser and Rocha [10] is a promising model for future study. The problem of a Fermi surface coupled to a gauge field appears to be under control in d = 3: the results of the self-consistent one-loop theory [75][76][77] are expected to be robust to higher order corrections [41,42].…”

“…In this section we consider models inspired by the case µ 1 = µ 2 = 0, µ 3 = 0, which leads to some qualitatively different physics. This case is related to the model studied by Gubser and Rocha [10]. For µ 1 = µ 2 = 0, µ 3 = 0, the charged scalars and fermions both have unit global U(1) charges.…”

Diffusion and butterfly velocity at finite density

“…Unlike the previous studies, we first study D ± at finite density without any approximation and deduce the property of D c and D e in the incoherent regime. We consider two holographic models: the linear axion model [27] and one of the axion-dilaton models [28,29] based on the Gubser-Rocha model [30]. We choose these models because both allow the analytic solutions and they are related in the sense that at zero density the axion-dilaton model undergoes the phase transition to the linear axion model if the momentum relaxation is weak.…”

“…It is based on the Einstein-Maxwell-Dilaton model so called the Gubser-Rocha model [30]. To include momentum relaxation effect, a graviton mass term breaking translational invariance was added to the action and the linear-T -resistivity was observed in this model [44].…”