Transport coefficients from hyperscaling violating black brane: shear viscosity and 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 $1/4π$ 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 $θ$. 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 $θ$. 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.