All order effective action for charge diffusion from Schwinger-Keldysh holography

TL;DR

This paper derives an all-order effective action for charge diffusion in a holographic model, incorporating thermal fluctuations and providing analytical and numerical transport coefficients.

Contribution

It introduces a systematic method to solve 5D Maxwell equations in a doubled Schwarzschild-AdS$_5$ geometry for charge diffusion.

Findings

Analytical expressions for transport coefficients in hydrodynamics.

Numerical results for finite momentum transport coefficients.

Identification of thermal fluctuation effects on charge current.

Abstract

An effective action for diffusion of a conserved $U(1)$ charge is derived to all orders in the derivative expansion within a holographic model dual to the Schwinger-Keldysh closed time path. A systematic approach to solution of the 5D Maxwell equations in a doubled Schwarzschild-AdS$_5$ black brane geometry is developed. Constitutive relation for the stochastic charge current is shown to have a term induced by thermal fluctuations (coloured noise). All transport coefficient functions parameterising the effective action and constitutive relations are computed analytically in the hydrodynamic expansion, and then numerically for finite momenta.