Goldstone bosons and fluctuating hydrodynamics with dipole and momentum conservation

TL;DR

This paper develops a novel effective field theory for fluids with conserved charge, dipole moments, and momentum, revealing unusual hydrodynamic modes, instabilities below four dimensions, and the Goldstone nature of momentum density.

Contribution

It introduces a Schwinger-Keldysh framework for dipole and momentum conserving fluids, uncovering unique hydrodynamic modes and symmetry-breaking phenomena not seen in conventional fluids.

Findings

Hydrodynamic modes include quadratic dispersion sound waves and subdiffusive decay.

Hydrodynamics is unstable below four spatial dimensions.

Momentum density acts as a Goldstone boson for a spontaneously broken dipole symmetry.

Abstract

We develop a Schwinger-Keldysh effective field theory describing the hydrodynamics of a fluid with conserved charge and dipole moments, together with conserved momentum. The resulting hydrodynamic modes are highly unusual, including sound waves with quadratic (magnon-like) dispersion relation and subdiffusive decay rate. Hydrodynamics itself is unstable below four spatial dimensions. We show that the momentum density is, at leading order, the Goldstone boson for a dipole symmetry which appears spontaneously broken at finite charge density. Unlike an ordinary fluid, the presence or absence of energy conservation qualitatively changes the decay rates of the hydrodynamic modes. This effective field theory naturally couples to curved spacetime and background gauge fields; in the flat spacetime limit, we reproduce the "mixed rank tensor fields" previously coupled to fracton matter.