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

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 Alfvén and magnetosonic waves are discussed.