Null Fluids - A New Viewpoint of Galilean Fluids

TL;DR

This paper introduces null fluids as a relativistic framework that corresponds to Galilean fluids in lower dimensions, providing a new perspective on their symmetries, thermodynamics, and anomalies through light cone reduction.

Contribution

It establishes a one-to-one correspondence between null fluids and Galilean fluids, extending the equilibrium partition function to include anomalies via light cone reduction.

Findings

Null fluids are in one-to-one correspondence with Galilean fluids.

The symmetries, thermodynamics, and constitutive relations are identical for null and Galilean fluids.

A mechanism to incorporate U(1) anomalies in Galilean theories is developed.

Abstract

This article is a detailed version of our short letter `On equilibrium partition function for non-relativistic fluid' [arXiv:1505.05677] extended to include an anomalous $U(1)$ symmetry. We construct a relativistic system, which we call null fluid and show that it is in one-to-one correspondence with a Galilean fluid living in one lower dimension. The correspondence is based on light cone reduction, which is known to reduce the Poincare symmetry of a theory to Galilean in one lower dimension. We show that the proposed null fluid and the corresponding Galilean fluid have exactly same symmetries, thermodynamics, constitutive relations, and equilibrium partition to all orders in derivative expansion. We also devise a mechanism to introduce $U(1)$ anomaly in even dimensional Galilean theories using light cone reduction, and study its effect on the constitutive relations of a Galilean Fluid.