Generating Temperature Flow for eta/s with Higher Derivatives: From Lifshitz to AdS

TL;DR

This paper studies how higher derivative corrections affect the shear viscosity to entropy density ratio in charged dilatonic black branes, revealing a temperature-dependent flow from Lifshitz to AdS geometries with implications for dual plasma behavior.

Contribution

It introduces a model where eta/s flows with temperature due to the interpolation between Lifshitz-like and AdS geometries, incorporating higher derivative effects and scalar couplings.

Findings

eta/s varies with temperature, influenced by the dynamical exponent z

Higher derivative corrections induce additional temperature dependence in eta/s

The IR behavior of eta/s is significantly affected by scalar couplings to higher derivatives

Abstract

We consider charged dilatonic black branes in AdS_5 and examine the effects of perturbative higher derivative corrections on the ratio of shear viscosity to entropy density eta/s of the dual plasma. The structure of eta/s is controlled by the relative hierarchy between the two scales in the plasma, the temperature and the chemical potential. In this model the background near-horizon geometry interpolates between a Lifshitz-like brane at low temperature, and an AdS brane at high temperatures -- with AdS asymptotics in both cases. As a result, in this construction the viscosity to entropy ratio flows as a function of temperature, from a value in the IR which is sensitive to the dynamical exponent z, to the simple result expected for an AdS brane in the UV. Coupling the scalar directly to the higher derivative terms generates additional temperature dependence, and leads to a particularly interesting structure for eta/s in the IR.