Fracton magnetohydrodynamics

TL;DR

This paper develops a new framework called fracton magnetohydrodynamics, extending hydrodynamics with multipolar symmetries to systems with gauged symmetries, revealing the origin of hydrodynamic modes through higher-form symmetries.

Contribution

It introduces fracton MHD derived from higher-rank Maxwell's equations, connecting symmetries to hydrodynamic modes and enabling exploration of exotic hydrodynamic theories.

Findings

Fracton MHD arises from higher-rank Maxwell's equations.

Hydrodynamic modes are linked to higher-form symmetries.

The approach can identify exotic hydrodynamic theories.

Abstract

We extend recent work on hydrodynamics with global multipolar symmetries -- known as "fracton hydrodynamics" -- to systems in which the multipolar symmetries are gauged. We refer to the latter as "fracton magnetohydrodynamics", in analogy to conventional magnetohydrodynamics (MHD), which governs systems with gauged charge conservation. We show that fracton MHD arises naturally from higher-rank Maxwell's equations and in systems with one-form symmetries obeying certain constraints; while we focus on "minimal" higher-rank generalizations of MHD that realize diffusion, our methods may also be used to identify other, more exotic hydrodynamic theories (e.g., with magnetic subdiffusion). In contrast to semi-microscopic derivations of MHD, our approach elucidates the origin of the hydrodynamic modes by identifying the corresponding higher-form symmetries. Being rooted in symmetries, the hydrodynamic modes may persist even when the semi-microscopic equations no longer provide an accurate description of the system.