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

Understand

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.