Transport coefficients, membrane couplings and universality at extremality

TL;DR

This paper introduces an efficient holographic method to compute zero-frequency transport coefficients in strongly coupled theories with higher derivative gravity, revealing universal behaviors at extremality.

Contribution

It provides analytic formulas for transport coefficients in higher derivative gravity theories and demonstrates their universal properties at zero temperature and finite chemical potential.

Findings

Shear viscosity to entropy ratio is universally 1/4π.

Zero frequency conductivity's real part is universally zero.

Higher derivative corrections do not alter these universal results.

Abstract

We present an efficient method for computing the zero frequency limit of transport coefficients in strongly coupled field theories described holographically by higher derivative gravity theories. Hydrodynamic parameters such as shear viscosity and conductivity can be obtained by computing residues of poles of the off-shell lagrangian density. We clarify in which sense these coefficients can be thought of as effective couplings at the horizon, and present analytic, Wald-like formulae for the shear viscosity and conductivity in a large class of general higher derivative lagrangians. We show how to apply our methods to systems at zero temperature but finite chemical potential. Our results imply that such theories satisfy $\eta/s=1/4\pi$ universally in the Einstein-Maxwell sector. Likewise, the zero frequency limit of the real part of the conductivity for such systems is shown to be universally zero, and we conjecture that higher derivative corrections in this sector do not modify this result to all orders in perturbation theory.