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

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.