Peculiar properties of a charged dilatonic black hole in AdS_5

TL;DR

The paper constructs and analyzes a charged dilatonic black hole in $AdS_5$ with a dilaton-modified gauge kinetic term, showing low-temperature linear entropy and normal-mode fermionic excitations that resemble Fermi-liquid behavior. It provides analytic control by embedding the solution in string theory via spinning D3-branes, exposes a Gregory-Laflamme–type thermodynamic instability in the 5D lift, and identifies an $AdS_3$ near-horizon factor in the ten-dimensional lift that links the thermodynamics to 1+1D conformal dynamics. The work extends to $AdS_4$ analogues and presents scaling solutions with tunable entropy–temperature power laws, suggesting a broader class of holographic IR behaviors that could realize generalized Fermi-liquid physics under suitable embeddings. Overall, the results indicate that such dilatonic black holes, or their IR relatives, are plausible holographic duals of Fermi liquids, albeit with caveats related to stability and the specific string-theory embedding.

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.

Figures (1)

• Figure 1: A normal mode with $u^+_2$ nonzero (corresponding to a pole in $G_{22}$) for $m=0$, $Q/L=1$, $q/L=2$ and $k/\Omega=3/2$. The solid line corresponds to $u^+_2$, which is purely real. For this normal mode $u^+_1$ and $u^-_2$ are exactly zero and $u^-_1$ is purely imaginary (the analytical forms are given in \ref{['GotNormalMode']}). The dashed lines show the real (Red) and imaginary (Green) parts of the purely infalling solution for $L\omega=10^{-3}$. Note that they match away from $r=0$ and differ for small $r$, where the terms proportional to $\omega$ in \ref{['Diracb']} become dominant.