Power Law of Shear Viscosity in Einstein-Maxwell-Dilaton-Axion model

TL;DR

This paper explores the temperature dependence of shear viscosity to entropy density ratio in charged black hole solutions with hyperscaling violation, revealing a power law behavior influenced by relevant currents.

Contribution

It constructs new black hole solutions with hyperscaling violation and numerically verifies the power law behavior of shear viscosity ratio at low temperatures.

Findings

The ratio follows a power law $ au/s \\sim T^\\kappa$ at low T.

The exponent \\kappa is unaffected by irrelevant currents.

The exponent \\kappa is reduced by relevant currents.

Abstract

We construct charged black hole solutions with hyperscaling violation in the infrared(IR) region in Einstein-Maxwell-Dilaton-Axion theory and investigate the temperature behavior of the ratio of holographic shear viscosity to the entropy density. When translational symmetry breaking is relevant in the IR, the power law of the ratio is testified numerically at low temperature $T$, namely, $\eta/s\sim T^\kappa$, where the values of exponent $\kappa$ coincide with the analytical results. We also find that the exponent $\kappa$ is not affected by irrelevant current, but is reduced by the relevant current.