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

TL;DR

This work extends holographic duality to theories with generalised global (higher-form) symmetries by constructing a bulk dual with gravity and a two-form field in a magnetised background, effectively coupling a strongly interacting matter sector to dynamical electromagnetism. It develops a holographic dictionary for higher-form symmetries, computes the equation of state and first-order transport coefficients, and uses these inputs to study magnetohydrodynamic waves (Alfvén and magnetosonic) across weak to strong magnetic fields. Key findings include a universal transverse shear viscosity to entropy density ratio $\eta_{\perp}/s = 1/(4\pi)$, and rich angle-dependent MHD phenomenology with mode transmutation and complex-frequency dynamics. The results provide a microscopic, holographic description of MHD in a dense, strongly coupled plasma and illustrate how dynamical boundary electromagnetism shapes transport and wave propagation in novel regimes relevant to strongly magnetised systems.

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.

Figures (13)

• Figure 1: Dimensionless energy density $\varepsilon/\mathcal{B}^2$ (top-left), pressure $p/\mathcal{B}^2$ (top-right), entropy density $s/\mathcal{B}^{3/2}$ (bottom-left) and chemical potential $\mu/\mathcal{B}$ (bottom-right), in units of $N_c^2 / (2\pi^2)$, plotted as a function of the dimensionless parameter $T/\sqrt{\mathcal{B}}$. The first three plots use logarithmic scales on both axes.
• Figure 2: The plots of (dimensionless) first-order transport coefficients as a function of $T / \sqrt{\mathcal{B}}$.
• Figure 3: The critical angle $\theta_c$ for Alfvén waves (left) and slow magnetosonic waves (right), plotted as a function of $T/\sqrt{\mathcal{B}}$ for $k/\sqrt{\mathcal{B}} = \{0.1, \, 0.2, \,0.4, \, 0.6 \}$. The dashed line at the top of both sub-figures indicates the value of $\theta_c = \pi/2$.
• Figure 4: Diagrams depicting the $\theta$-dependent pattern of transmutation from sound to diffusive modes for Alfvén waves and slow and fast magnetosonic waves. The left and right diagrams correspond to weak- and strong-field regimes. The relevant dispersion relation are stated in Eqs. \ref{['specialSound']} and \ref{['specialDiffuse']}.
• Figure 5: Angular dependence of the speeds of Alfvén (black, solid), fast (blue, dotted) and slow (red, dashed) magnetosonic waves in the strong-field, the crossover and the weak-field regimes.