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

TL;DR

The paper develops a dissipationless hydrodynamics framework as an effective field theory with Goldstone modes $\phi^I$ and $\psi$, enforcing a symmetry-based derivative expansion and mapping EFT variables to standard thermodynamics. It shows that one-derivative non-dissipative corrections are absent or removable by field redefinitions, and provides a concrete second-order example illustrating how corrections influence the sound dispersion. The approach yields a clean, symmetry-driven dictionary between field theory and hydrodynamics, and sets the stage for incorporating anomalies and dissipation via additional sectors or Wess-Zumino terms in follow-up work. Overall, it offers a principled EFT perspective on dissipationless fluids with conserved charges and a path toward more complete hydrodynamic theories.

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.