Effective field theory for hydrodynamics: thermodynamics, and the derivative expansion

TL;DR

This paper develops an effective field theory framework for non-dissipative hydrodynamics, incorporating conserved charges and systematic derivative expansion, providing a basis for studying anomalies and corrections to sound waves.

Contribution

It extends previous hydrodynamic effective field theories to include conserved charges and clarifies the thermodynamic-field theory correspondence.

Findings

Derived correction to sound-wave dispersion relation from second-order terms

Established a systematic derivative expansion scheme for hydrodynamics

Set the stage for analyzing anomalies in hydrodynamics using EFT

Abstract

We consider the low-energy effective field theory describing the infrared dynamics of non-dissipative fluids. We extend previous work to accommodate conserved charges, and we clarify the matching between field theory variables and thermodynamical ones. We discuss the systematics of the derivative expansion, for which field theory offers a conceptually clear and technically neat scheme. As an example, we compute the correction to the sound-wave dispersion relation coming from a sample second-order term. This formalism forms the basis for a study of anomalies in hydrodynamics via effective field theory, which is initiated in a companion paper.