Aspects of hot Galilean field theory

TL;DR

This paper develops a covariant formulation of Galilean-invariant thermal field theory, explores its hydrodynamics and partition functions, and provides new insights into non-relativistic fluids, especially in two dimensions with parity violation.

Contribution

It introduces a covariant approach to Galilean hydrodynamics coupled to background spacetime and clarifies the relation between entropy current constraints and hydrostatic partition functions.

Findings

Derived detailed hydrodynamics for Galilean theories.

Calculated partition functions for parity-violating fluids in 2D.

Established correspondence between entropy current constraints and hydrostatic partition functions.

Abstract

We reconsider general aspects of Galilean-invariant thermal field theory. Using the proposal of our companion paper, we recast non-relativistic hydrodynamics in a manifestly covariant way and couple it to a background spacetime. We examine the concomitant consequences for the thermal partition functions of Galilean theories on a time-independent, but weakly curved background. We work out both the hydrodynamics and partition functions in detail for the example of parity-violating normal fluids in two dimensions to first order in the gradient expansion, finding results that differ from those previously reported in the literature. As for relativistic field theories, the equality-type constraints imposed by the existence of an entropy current appear to be in one-to-one correspondence with those arising from the existence of a hydrostatic partition function. Along the way, we obtain a number of useful results about non-relativistic hydrodynamics, including a manifestly boost-invariant presentation thereof, simplified Ward identities, the systematics of redefinitions of the fluid variables, and the positivity of entropy production.