Effective field theories of dissipative fluids with one-form symmetries

TL;DR

This paper develops a comprehensive effective field theory framework for dissipative fluids with one-form symmetries, including string fluids and magnetohydrodynamics, highlighting the role of discrete symmetries and spontaneous symmetry breaking.

Contribution

It classifies and constructs the most general EFTs for one-form symmetry fluids, revealing distinct diffusive behaviors and connecting spontaneous symmetry breaking to Maxwell theory.

Findings

Two types of diffusive transport depending on discrete symmetries.

Effective actions enable dispersion relation calculations up to cubic order.

Spontaneous breaking of one-form symmetry reduces to Maxwell theory.

Abstract

A system with a one-form global symmetry at finite temperature can be viewed as a dissipative fluid of string-like objects. In this work, we classify and construct the most general effective field theories for hydrodynamics of such string fluids, in a probe limit where the one-form charge density is decoupled from the energy-momentum tensor. We show that at leading order in the derivative expansion, there are two distinct types of diffusive transport in a string fluid depending on the discrete spacetime symmetries present in it. One particular application of interest is magnetohydrodynamics (MHD), where the effective field theories describe the diffusion of magnetic field lines. Due to the distinction between the effective field theories for different discrete symmetries, we show that the MHD of a fluid with charge conjugation symmetry is qualitatively different from that of a neutron star, which we previously discussed in arXiv:2207.01636. The explicit effective actions that we write down can be used to obtain the dispersion relations $\omega(k)$ up to cubic order in momenta for each of the different discrete symmetry choices. As another application of this formalism, we show that when the one-form symmetry is spontaneously broken, the effective action reduces to the Maxwell theory. This confirms the interpretation of the photon as a Goldstone boson arising from the spontaneous breaking of a one-form symmetry.