An effective description of momentum diffusion in a charged plasma from holography

TL;DR

This paper develops an effective field theory for momentum diffusion in a charged plasma using holography, analyzing fluctuations around a Reissner-Nordstrom-AdS black hole to connect gravitational dynamics with hydrodynamic transport properties.

Contribution

It introduces a holographic effective field theory framework for low-lying modes in a charged plasma, decoupling momentum and charge transport modes, and deriving the quadratic action governing their hydrodynamics.

Findings

Derived the effective action for charge and momentum fluctuations.

Identified a length scale related to Ohmic conductivity.

Connected gravitational fluctuations to transport coefficients.

Abstract

We discuss the physics of momentum diffusion in a charged plasma. Following the holographic strategy outlined in arXiv:2012.03999 we construct an open effective field theory for the low-lying modes of the conserved currents. The charged plasma is modeled holographically in terms of a Reissner-Nordstrom-AdS black hole. We analyze graviton and photon fluctuations about this background, decoupling in the process the long-lived momentum diffusion mode from the short-lived charged transport mode. Furthermore, as in the aforementioned reference, we argue that the dynamics of these modes are captured by a set of designer scalars in the background geometry. These scalars have their gravitational coupling modulated by an auxiliary dilaton with long-lived modes being weakly coupled near the spacetime asymptopia. Aided by these observations, we obtain the quadratic effective action that governs the fluctuating hydrodynamics of charge current and stress tensor, reproducing in the process transport data computed previously. We also point out an interesting length scale lying between the inner and outer horizon radii of the charged black hole associated with Ohmic conductivity.