Dissipative hydrodynamics with higher-form symmetry

TL;DR

This paper develops a first-order dissipative hydrodynamics framework for fluids with higher-form symmetries, revealing new transport coefficients and anisotropic behaviors relevant to string charge fluids and magnetohydrodynamics.

Contribution

It introduces a novel first-order dissipative hydrodynamics theory for fluids with $q$-form symmetry, identifying new transport coefficients and analyzing anisotropic effects and interfaces.

Findings

Identified $q$+7 parity-even transport coefficients for $q>1$.

Discovered additional shear viscosity and resistivity coefficients in higher-form fluids.

Analyzed capillary wave dispersion revealing anisotropic signatures.

Abstract

A theory of parity-invariant dissipative fluids with $q$-form symmetry is formulated to first order in a derivative expansion. The fluid is anisotropic with symmetry $\text{SO}(D-1-q)\times\text{SO}(q)$ and carries dissolved $q$-dimensional charged objects that couple to a $(q+1)$-form background gauge field. The case $q=1$ for which the fluid carries string charge is related to magnetohydrodynamics in $D=4$ spacetime dimensions. We identify $q$+7 parity-even independent transport coefficients at first order in derivatives for $q>1$. In particular, compared to the $q=1$ case under the assumption of parity and charge conjugation invariance, fluids with $q>1$ are characterised by $q$ extra transport coefficients with the physical interpretation of shear viscosity in the $\text{SO}(q)$ sector and current resistivities. We discuss certain issues related to the existence of a hydrostatic sector for fluids with higher-form symmetry for any $q\ge1$. We extend these results in order to include an interface separating different fluid phases and study the dispersion relation of capillary waves finding clear signatures of anisotropy. The formalism developed here can be easily adapted to study hydrodynamics with multiple higher-form symmetries.