Hydrodynamics with conserved current from the gravity dual

TL;DR

This paper derives the hydrodynamic behavior of a conserved current using gauge/gravity duality, showing that Einstein equations encode boundary conservation laws and calculating conductivities consistent with the Wiedemann-Franz law.

Contribution

It provides a novel derivation of hydrodynamics with conserved current from gravity duals, linking Einstein equations to boundary conservation laws and computing conductivities.

Findings

Thermal and electric conductivities are explicitly calculated.

Wiedemann-Franz law holds with Lorentz number 1/e^2.

Bulk Einstein equations encode boundary conservation laws.

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 $1/e^2$