Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm

TL;DR

This paper demonstrates that the low-frequency response of strongly coupled field theories at finite temperature can be universally described by the horizon geometry of their gravity duals, linking boundary transport properties to black hole mechanics.

Contribution

It provides a general proof of the universality of shear viscosity and introduces flow equations for transport coefficient evolution beyond the low-frequency limit.

Findings

Transport coefficients are determined by horizon geometry.

Universal shear viscosity is linked to gravitational couplings.

Flow equations describe nontrivial evolution from horizon to boundary.

Abstract

We show that at the level of linear response the low frequency limit of a strongly coupled field theory at finite temperature is determined by the horizon geometry of its gravity dual, i.e. by the "membrane paradigm" fluid of classical black hole mechanics. Thus generic boundary theory transport coefficients can be expressed in terms of geometric quantities evaluated at the horizon. When applied to the stress tensor this gives a simple, general proof of the universality of the shear viscosity in terms of the universality of gravitational couplings, and when applied to a conserved current it gives a new general formula for the conductivity. Away from the low frequency limit the behavior of the boundary theory fluid is no longer fully captured by the horizon fluid even within the derivative expansion; instead we find a nontrivial evolution from the horizon to the boundary. We derive flow equations governing this evolution and apply them to the simple examples of charge and momentum diffusion.