Generalised global symmetries in holography: magnetohydrodynamic waves in a strongly interacting plasma

TL;DR

This paper develops a holographic dual framework for strongly coupled plasmas with higher-form symmetries, enabling analysis of magnetohydrodynamic waves and their behavior under various magnetic field strengths.

Contribution

It constructs a holographic model for dissipative MHD with higher-form symmetries, providing the first microscopic description of MHD wave phenomenology in strongly interacting plasmas.

Findings

Computed the equation of state and transport coefficients for the dual plasma.

Analyzed the behavior of Alfvén and magnetosonic waves across magnetic field strengths.

Predicted wave behaviors in strongly coupled, dense plasmas.

Abstract

We begin the exploration of holographic duals to theories with generalised global (higher-form) symmetries. In particular, we focus on the case of magnetohydrodynamics (MHD) in strongly coupled plasmas by constructing and analysing a holographic dual to a recent, generalised global symmetry-based formulation of dissipative MHD. The simplest holographic dual to the effective theory of MHD that was proposed as a description of plasmas with any equation of state and transport coefficients contains dynamical graviton and two-form gauge field fluctuations in a magnetised black brane background. The dual field theory, which is closely related to the large-$N_c$, $\mathcal{N} = 4$ supersymmetric Yang-Mills theory at (infinitely) strong coupling, is, as we argue, in our setup coupled to a dynamical $U(1)$ gauge field with a renormalisation condition-dependent electromagnetic coupling. After constructing the holographic dictionary for gauge-gravity duals of field theories with higher-form symmetries, we compute the dual equation of state and transport coefficients, and for the first time analyse phenomenology of MHD waves in a strongly interacting, dense plasma with a (holographic) microscopic description. From weak to extremely strong magnetic fields, several predictions for the behaviour of Alfv\'{e}n and magnetosonic waves are discussed.