Hydrodynamics of dilation and spin currents

TL;DR

This paper develops a relativistic hydrodynamic framework for fluids with spin and dilation charges, revealing unique excitations and effects relevant to conformal fluids and cosmological phenomena.

Contribution

It introduces a novel hydrodynamic theory incorporating dilation charges and their dynamics, including entropy analysis and coupling to electromagnetic fields.

Findings

Identification of a gapped dilation excitation.

Discovery of freeze-out of sound modes in the relativistic regime.

Extension to nonrelativistic microstretch fluid limit.

Abstract

We formulate a relativistic hydrodynamic theory for fluids with spin and intrinsic dilation charges. Using an entropy-current analysis, we derive constitutive relations featuring a bulk viscosity and a dilation conductivity governing the relaxation and diffusion of dilation charge. Linear mode analysis reveals a gapped dilation excitation and the freeze-out of long-wavelength sound modes, similar to the superhorizon modes in cosmology. In the nonrelativistic limit, the theory reduces to that of microstretch fluids. Upon coupling to electromagnetic field, we show that the scale anomaly permits additional contributions in the electric current, dilation current, and energy-momentum tensor. Our theory naturally applies to nearly conformal fluids undergoing rapid expansion or contraction.