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Hydrodynamics of higher-rank gauge theories

by Marvin Qi, Oliver Hart, Aaron J. Friedman, Rahul Nandkishore, Andrew Lucas

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Submission summary

Authors (as registered SciPost users): Aaron Friedman · Oliver Hart · Rahul Nandkishore
Submission information
Preprint Link: scipost_202210_00035v1  (pdf)
Date accepted: 2022-10-07
Date submitted: 2022-10-04 03:22
Submitted by: Hart, Oliver
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
Approach: Theoretical


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.

Author comments upon resubmission

We thank all the referees for their positive assessment of our resubmitted manuscript. To satisfy the concerns of the third referee, we have modified the title to "Hydrodynamics of higher-rank gauge theories". This should remove any confusion that may have been caused by the use of the term "magnetohydrodynamics" in the title.

List of changes

Title changed from "Fracton magnetohydrodynamics" to "Hydrodynamics of higher-rank gauge theories".

Published as SciPost Phys. 14, 029 (2023)

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