The role of Weyl symmetry in hydrodynamics

TL;DR

This paper explores how Weyl symmetry can be incorporated into relativistic hydrodynamics, revealing its gauge structure, the emergence of Weyl gauge fields from fluid degrees of freedom, and establishing local charge conservation laws.

Contribution

It demonstrates the implementation of Weyl symmetry via minimal coupling in hydrodynamics and identifies the Weyl gauge connection as arising from fluid expansion and entropy gradients.

Findings

Weyl gauge connection is derived from fluid expansion and entropy gradients.

The minimal coupling prescription correctly handles curvature in hydrodynamics.

A local charge and current conservation law is established for Weyl symmetry in fluids.

Abstract

This article is dedicated to the analysis of Weyl symmetry in the context of relativistic hydrodynamics. Here is discussed how this symmetry is properly implemented using the prescription of minimal coupling: $\partial\to \partial +\omega \mathcal{A}$. It is shown that this prescription has no problem to deal with curvature since it gives the correct expressions for the commutator of covariant derivatives. In the hydrodynamics the Weyl gauge connection emerges from the degrees of freedom of the fluid: it is a combination of the expansion and entropy gradient. The remaining degrees of the fluid and the metric tensor are see in this context as charged fields under the Weyl gauge connection. The gauge nature of conformal hydrodynamics is emphasized and a charge for the Weyl connection is defined. A notion of local charge and current densities are considered and a local charge conservation law is reached.