Effective field theory for hydrodynamics without boosts

TL;DR

This paper develops a covariant effective field theory for hydrodynamics without boost symmetry, characterizing transport phenomena and analyzing fluctuation spectra in anisotropic states, applicable to various non-Lorentzian fluids.

Contribution

It introduces a boostless hydrodynamic EFT with detailed transport coefficients and a stable hydrodynamic frame, unifying Lorentzian, Galilean, and Lifshitz fluids.

Findings

29 independent transport coefficients identified

Distinct sound and shear modes analyzed

Stable hydrodynamic frame established

Abstract

We formulate the Schwinger-Keldysh effective field theory of hydrodynamics without boost symmetry. This includes a spacetime covariant formulation of classical hydrodynamics without boosts with an additional conserved particle/charge current coupled to Aristotelian background sources. We find that, up to first order in derivatives, the theory is characterised by the thermodynamic equation of state and a total of 29 independent transport coefficients, in particular, 3 hydrostatic, 9 non-hydrostatic non-dissipative, and 17 dissipative. Furthermore, we study the spectrum of linearised fluctuations around anisotropic equilibrium states with non-vanishing fluid velocity. This analysis reveals a pair of sound modes that propagate at different speeds along and opposite to the fluid flow, one charge diffusion mode, and two distinct shear modes along and perpendicular to the fluid velocity. We present these results in a new hydrodynamic frame that is linearly stable irrespective of the boost symmetry in place. This provides a unified covariant stable approach for simultaneously treating Lorentzian, Galilean, and Lifshitz fluids within an effective field theory framework and sets the stage for future studies of non-relativistic intertwined patterns of symmetry breaking.