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Effective field theory for hydrodynamics without boosts

by Jay Armas, Akash Jain

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Submission summary

As Contributors: Jácome Armas · Akash Jain
Arxiv Link: (pdf)
Date accepted: 2021-09-02
Date submitted: 2021-08-10 04:45
Submitted by: Jain, Akash
Submitted to: SciPost Physics
Academic field: Physics
  • Fluid Dynamics
  • High-Energy Physics - Theory
Approach: Theoretical


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.

Published as SciPost Phys. 11, 054 (2021)

Author comments upon resubmission

We have fixed some references and typos according to the referees' suggestions.

List of changes

1. Fixed typos in eq. (2.9), below eq. (2.28), and in the first paragraph of section 6.
2. Added clarifying comments on page 3, in footnote 3, above eq. (2.14), and below eq. (2.31).
3. Fixed citations on page 3 and in section 2.2.3.

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