Transport coefficients from hyperscaling violating black brane: shear viscosity and conductivity

TL;DR

This paper studies shear viscosity and conductivity in a non-relativistic boundary theory dual to a hyperscaling violating black brane, revealing universal ratios and frequency-dependent behaviors influenced by geometrical parameters.

Contribution

It provides universal formulas for AC conductivity and confirms the shear viscosity to entropy density ratio always satisfies the KSS bound in this setup.

Findings

Shear viscosity to entropy density ratio is always 1/4π.

AC conductivity depends on parameters z and θ, with high-frequency behavior varying.

Temperature does not affect high-frequency scaling but influences low-frequency conductivity.

Abstract

We investigate two transport coefficients, shear viscosity and conductivity, in a non-relativistic boundary filed theory without hyperscaling symmetry, which is dual to a bulk charged hyperscaling violating black brane. Employing matching method, we obtain that the ratio of shear viscosity and the entropy density is alway $1/4\pi$ at any temperature, which satisfies the Kovtun-Starinets-Son (KSS) bound. Besides, we also present the universal formulas of AC conductivity, which is closely dependent on the relation between geometrical parameters $z$ and $\theta$. The optical conductivity at high frequency limit behaves with a (non)-power law scaling or approaches to be constant, depending on the choice of $z$ and $\theta$. This feature is different from the observes in Lifshitz black brane that the optical conductivity always complies with a (non)-power law scaling in high frequency limit when the Lifshitz exponent $z>1$. We also argue that the temperate has no print on the exponent of (non)-power law scaling in large frequency while it will affect the strength of conductivity at low frequency.