Hydrodynamics as the effective field theory of strong-to-weak spontaneous symmetry breaking

TL;DR

This paper develops an effective field theory linking hydrodynamics to strong-to-weak spontaneous symmetry breaking, revealing diffusion as a Goldstone mode and providing insights into the symmetries of normal fluids.

Contribution

It introduces a novel EFT framework for SWSSB of a U(1) symmetry, connecting hydrodynamics with symmetry breaking and Goldstone modes.

Findings

Diffusion mode identified as Goldstone boson

Hydrodynamics viewed as superfluidity of broken symmetry

Reparameterization symmetries explained physically

Abstract

Inspired by the hunt for new phases of matter in quantum mixed states, it has recently been proposed that the equivalence of microcanonical and canonical ensembles in statistical mechanics is a manifestation of strong-to-weak spontaneous symmetry breaking (SWSSB) in an underlying many-body quantum description. Here, we build an effective field theory for SWSSB of a global U(1) symmetry; the answer exactly reproduces the Schwinger-Keldysh effective field theory of diffusion for the conserved charge. We conclude that hydrodynamics can be understood as a theory of "superfluidity" for the broken strong symmetry: a non-vanishing susceptibility is a measurable order parameter for SWSSB, the diffusion mode is the Goldstone boson of the spontaneously broken continuous symmetry, and a generalization of Goldstone's Theorem implies that the diffusion mode is always long-lived. This perspective provides a transparent physical explanation for the unusual "reparameterization" symmetries which are a necessary ingredient of Schwinger-Keldysh effective field theories for "normal fluids".