Holography of Charged Dilaton Black Holes

TL;DR

The paper examines charged dilaton black branes in AdS4, revealing a Lifshitz-like near-horizon region with z determined by the dilaton coupling α and demonstrating an attractor mechanism that yields vanishing extremal entropy yet positive specific heat. By constructing AdS4 asymptotics through controlled perturbations, it shows a universal IR structure independent of asymptotic moduli and derives a Schrödinger-form equation for gauge perturbations to compute conductivity, finding σ(ω) ∝ ω^2 at T=0, irrespective of α. The work connects thermodynamic scaling, UV completions, and transport in a holographic setting, with potential implications for insulator-like behavior and non-Fermi liquid physics in the dual field theory. It also outlines extensions to magnetic, dyonic, and axionic cases, suggesting a broad, universal framework for IR dynamics in dilatonic AdS branes.

Abstract

We study charged dilaton black branes in $AdS_4$. Our system involves a dilaton $φ$ coupled to a Maxwell field $F_{μν}$ with dilaton-dependent gauge coupling, ${1\over g^2} = f^2(φ)$. First, we find the solutions for extremal and near extremal branes through a combination of analytical and numerical techniques. The near horizon geometries in the simplest cases, where $f(φ) = e^{αφ}$, are Lifshitz-like, with a dynamical exponent $z$ determined by $α$. The black hole thermodynamics varies in an interesting way with $α$, but in all cases the entropy is vanishing and the specific heat is positive for the near extremal solutions. We then compute conductivity in these backgrounds. We find that somewhat surprisingly, the AC conductivity vanishes like $ω^2$ at T=0 independent of $α$. We also explore the charged black brane physics of several other classes of gauge-coupling functions $f(φ)$. In addition to possible applications in AdS/CMT, the extremal black branes are of interest from the point of view of the attractor mechanism. The near horizon geometries for these branes are universal, independent of the asymptotic values of the moduli, and describe generic classes of endpoints for attractor flows which are different from $AdS_2\times R^2$.

Figures (2)

• Figure 1: Numerical solution interpolating between the near horizon solution and $AdS_4$ for $\alpha=1$ and $d_1 =-.514219$. The second plot shows that $a'(r)$ and $b'(r)$ approach $1$. Solid lines denote $a$, dashed lines denote $b$.
• Figure 2: Numerical solution for $\phi$, for $\alpha=1$.