Transport coefficients, membrane couplings and universality at extremality

TL;DR

This work develops a general, efficient framework for computing zero-frequency transport coefficients in strongly coupled holographic theories with higher-derivative gravity. By focusing on horizon data through a pole-residue (pole) method and generalized canonical momentum, it derives Wald-like analytic formulae for shear viscosity and DC conductivity that remain valid beyond two derivatives and clarifies their relation to membrane couplings. It demonstrates universality results at extremality, showing $\eta/s=1/(4\pi)$ in Einstein–Maxwell sectors and a zero low-frequency real conductivity that persists to all orders in higher-derivative corrections, under certain conditions. The findings refine prior proposals, extend the analysis to extremal backgrounds with $AdS_2$ near-horizon geometry, and outline potential extensions to Lifshitz spacetimes and fermionic correlators, offering a practical toolkit for holographic transport calculations in complex gravity theories.

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 $η/s=1/4π$ 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.