Transport Coefficients from Extremal Gauss-Bonnet Black Holes

TL;DR

This paper computes transport coefficients like shear viscosity and DC conductivity for strongly coupled field theories dual to Gauss-Bonnet gravity at zero temperature, revealing universal ratios and behaviors similar to Einstein gravity.

Contribution

It extends the calculation of shear viscosity and conductivity to zero temperature in Gauss-Bonnet gravity, showing the viscosity ratio remains universal and analyzing the effective coupling of transverse gravitons.

Findings

Shear viscosity to entropy density ratio remains at 1/4π at zero temperature.

DC conductivity's real part vanishes up to a delta function at zero temperature.

Shear viscosity is determined by the effective coupling of transverse gravitons.

Abstract

We calculate the shear viscosity of strongly coupled field theories dual to Gauss-Bonnet gravity at zero temperature with nonzero chemical potential. We find that the ratio of the shear viscosity over the entropy density is $1/4\pi$, which is in accordance with the zero temperature limit of the ratio at nonzero temperatures. We also calculate the DC conductivity for this system at zero temperature and find that the real part of the DC conductivity vanishes up to a delta function, which is similar to the result in Einstein gravity. We show that at zero temperature, we can still have the conclusion that the shear viscosity is fully determined by the effective coupling of transverse gravitons in a kind of theories that the effective action of transverse gravitons can be written into a form of minimally coupled scalars with a deformed effective coupling.