Holography and magnetohydrodynamics with dynamical gauge fields

TL;DR

This paper demonstrates that holographic models with mixed boundary conditions for gauge fields can accurately describe magnetohydrodynamics with dynamical gauge fields, matching theoretical predictions even at large magnetic fields.

Contribution

It introduces a holographic approach with dynamical boundary gauge fields using mixed boundary conditions, enabling the study of magnetohydrodynamics within this framework.

Findings

Holographic models match magnetohydrodynamics predictions at small electromagnetic coupling.

Perfect agreement observed between holography and magnetohydrodynamics in strong magnetic fields.

Dynamical gauge fields can be incorporated without higher-form bulk fields in holography.

Abstract

Within the framework of holography, the Einstein-Maxwell action with Dirichlet boundary conditions corresponds to a dual conformal field theory in presence of an external gauge field. Nevertheless, in many real-world applications, e.g., magnetohydrodynamics, plasma physics, superconductors, etc. dynamical gauge fields and Coulomb interactions are fundamental. In this work, we consider bottom-up holographic models at finite magnetic field and (free) charge density in presence of dynamical boundary gauge fields which are introduced using mixed boundary conditions. We numerically study the spectrum of the lowest quasi-normal modes and successfully compare the obtained results to magnetohydrodynamics theory in $2+1$ dimensions. Surprisingly, as far as the electromagnetic coupling is small enough, we find perfect agreement even in the large magnetic field limit. Our results prove that a holographic description of magnetohydrodynamics does not necessarily need higher-form bulk fields but can be consistently derived using mixed boundary conditions for standard gauge fields.