Charged Black Branes with Hyperscaling Violating Factor

TL;DR

The paper constructs an analytic hyperscaling-violating charged black brane in an Einstein–Maxwell–Dilaton theory with an exponential potential, providing a gravity dual for field theories with hyperscaling violation at finite temperature and density. The solution exhibits a metric with exponents $(z,\theta)$ and, at extremality, an $AdS_2\times \mathbb{R}^d$ near-horizon region, signaling an IR fixed point. Using holographic tools, the authors analyze entanglement entropy, fermion probes, and optical conductivity, revealing signatures of Fermi surfaces (including an $O(N^2)$ surface for $\theta=d-1$) and characteristic scaling $\text{Re}\,\sigma(\omega) \sim T^{(d-\theta)/z}$, with Drude-like features affected by impurities. They also discuss the (non)embeddability of the solution in string theory via known sphere reductions, suggesting further work with more fields or domain-wall potentials. Overall, the work broadens holographic models of hyperscaling violation at finite density and temperature and elucidates the IR structure and transport properties of these backgrounds.

Abstract

We present an analytic solution of a charged black hole with hyperscaling violating factor in an Einstein-Maxwell-Dilaton model where the scalar potential is key to the existence of a solution. This solution provides a candidate gravitational description of theories with hyperscaling violation at both finite temperature and finite charge density. Using this background we explore certain features of these theories via AdS/CFT correspondence. Finally, we discuss embeddings based on the well-known sphere reductions of ten and eleven-dimensional supergravity.

Figures (3)

• Figure 1: The behavior of spectral functions the for hyperscaling violating geometry with $\theta=1,z=2$ (left), and $\theta=0.4, z=1.4$ (right). To compare the results with that of RN AdS black brane we have also plotted this case which in our notation corresponds to $\theta=0,z=1$ (see Faulkner:2009wj).
• Figure 2: The real and imaginary parts of the conductivity versus $\omega$ for a fixed temperature. To find this plot we have set $Q=\sqrt{3}$, and $r_H=1.25$.
• Figure 3: The real part of the conductivity versus $r_H$ for a fixed frequency. To find this plot we have set $Q=\sqrt{3}$, and $\omega=0.001$. The numerical solution is shown by dots, while the best fit is drawn by a red line.