Hydrodynamics with conserved current from the gravity dual

TL;DR

Using gauge/gravity duality, the paper derives the form of hydrodynamics with a conserved current in a charged AdS background by promoting the black brane parameters to spacetime functions and performing a first-order derivative expansion. The authors show the bulk equations imply boundary energy-momentum and current conservation in the presence of an external electromagnetic field, and they extract transport coefficients from the first-order corrections. They obtain explicit expressions for the shear viscosity $\eta$, and the thermal and electric conductivities $\kappa$ and $\sigma$, finding the Wiedemann-Franz law $\kappa = \sigma T / e^2$ with Lorentz number $1/e^2$. The results express these transport coefficients in terms of horizon data and fundamental theory parameters, providing a holographic computation of dissipative hydrodynamics with a conserved current and suggesting extensions to other AdS/CFT setups and higher-order analyses.

Abstract

We determine the structure of the hydrodynamics with conserved current, using the gauge/gravity duality of charged black-hole background. It turns out that even in the presence of the external electromagnetic field at the boundary, bulk Einstein equation is equivalent to the boundary conservation of energy momentum tensor and that of current. As a consequence, the thermal conductivity and electric conductivity are calculated in terms of the parameters of the fundamental theory. We find that Wiedermann-Franz law hold with Lorentz number $1/e^2$

Figures (1)

• Figure 1: The coefficient of thermal conductivity or The electrical conductivity