On the Temperature Dependence of the Shear Viscosity and Holography

TL;DR

This paper investigates how shear viscosity to entropy density ratio eta/s varies with temperature in holographic models with scalar fields and higher derivative corrections, revealing conditions for minima related to phase transitions.

Contribution

It analyzes the temperature dependence of eta/s in holographic theories with scalar fields and higher derivatives, identifying geometric conditions for minima and their relation to phase transitions.

Findings

eta/s runs with temperature due to scalar profiles

Conditions for local and global minima of eta/s identified

Restrictions on higher derivative couplings derived

Abstract

We examine the structure of the shear viscosity to entropy density ratio eta/s in holographic theories of gravity coupled to a scalar field, in the presence of higher derivative corrections. Thanks to a non-trivial scalar field profile, eta/s in this setup generically runs as a function of temperature. In particular, its temperature behavior is dictated by the shape of the scalar potential and of the scalar couplings to the higher derivative terms. We consider a number of dilatonic setups, but focus mostly on phenomenological models that are QCD-like. We determine the geometric conditions needed to identify local and global minima for eta/s as a function of temperature, which translate to restrictions on the signs and ranges of the higher derivative couplings. Finally, such restrictions lead to an holographic argument for the existence of a global minimum for eta/s in these models, at or above the deconfinement transition.