An effective description of charge diffusion and energy transport in a charged plasma from holography

TL;DR

This paper uses holography to model a charged plasma, deriving an effective field theory for sound and charge diffusion modes, and providing detailed real-time response functions including fluctuations.

Contribution

It constructs an open effective field theory for low-lying modes in charged plasmas using holographic duality, decoupling phonon and charge diffusion modes.

Findings

Decoupling of phonon and charge diffusion modes.

Identification of current combinations for each mode.

Derivation of real-time Gaussian effective action with fluctuations.

Abstract

We discuss the physics of sound propagation and charge diffusion in a plasma with non-vanishing charge density. Our analysis culminates the program initiated in arXiv:2108.03244 to construct an open effective field theory of low-lying modes of the stress tensor and charge current in such plasmas. We model the plasma holographically as a Reissner-Nordstrom-AdS black hole, and study linearized fluctuations of longitudinally polarized scalar gravitons and photons in this background. We demonstrate that the perturbations can be decoupled and repackaged into the dynamics of two designer scalars, whose gravitational coupling is modulated by a non-trivial dilatonic factor. The holographic analysis allows us to isolate the phonon mode from the charge diffusion mode, and identify the combination of currents that corresponds to each of them. We use these results to obtain the real-time Gaussian effective action, which includes both the retarded response and the associated stochastic (Hawking) fluctuations, accurate to quartic order in gradients.