Novel Features of the Transport Coefficients in Lifshitz Black Branes

TL;DR

This paper investigates the transport properties of non-relativistic field theories dual to Lifshitz black branes with multiple U(1) gauge fields, revealing novel AC conductivity behavior and confirming the shear viscosity bound.

Contribution

It provides a systematic analysis of electric, thermal, and thermoelectric conductivities in Lifshitz holography with multiple gauge fields, highlighting new power law behaviors for z>1.

Findings

Nontrivial power law in electric AC conductivity for z>1

Shear viscosity to entropy density ratio respects the KSS bound

Relation between conductivity features and condensed matter models

Abstract

We study the transport coefficients, including the conductivities and shear viscosity of the non-relativistic field theory dual to the Lifshitz black brane with multiple U(1) gauge fields by virtue of the gauge/gravity duality. Focusing on the case of double U(1) gauge fields, we systematically investigate the electric, thermal and thermoelectric conductivities for the dual non-relativistic field theory. In the large frequency regime, we find a nontrivial power law behavior in the electric AC conductivity when the dynamical critical exponent z>1 in (2+1)-dimensional field theory. The relations between this novel feature and the `symmetric hopping model' in condensed matter physics are discussed. In addition, we also show that the Kovtun-Starinets-Son bound for the shear viscosity to the entropy density is not violated by the additional U(1) gauge fields and dilaton in the Lifshitz black brane.