Scale without conformal symmetry in hydrodynamics

TL;DR

This paper explores the properties of scale-invariant fluids lacking conformal symmetry, revealing unique hydrodynamic behaviors and the effects of dissipation and spontaneous symmetry breaking.

Contribution

It demonstrates that scale invariance without conformal symmetry leads to distinct hydrodynamic responses and clarifies the role of the virial current and dissipation effects.

Findings

Scale invariance without conformal symmetry results in an inhomogeneous conservation law.

Dissipation effects cause relaxation of hydrodynamic responses over long times.

Spontaneous breaking of scale symmetry does not introduce new hydrodynamic modes.

Abstract

Scale without conformal symmetry corresponds to an inhomogeneous conservation equation for the virial current sourced by the trace of the energy-momentum tensor. Fluids that are just scale-invariant differ qualitatively from their conformal counterparts, and generic dissipation effects relax the hydrodynamic response over sufficiently long time scales. Remarkably, this holds true already at the ideal order. Spontaneously broken scale symmetry does not, in general, add any new mode to the hydrodynamic sector.