Effective field theory for hydrodynamics without boosts

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.

Hydrodynamic effective field theories with discrete rotational symmetry

“…The main difference between our work and earlier work on the subject is that for a discrete point group, there are no continuous generators of rotational symmetry whatsoever. The key consequence of this is that, just as when one studies a non-relativistic fluid it is more appropriate to couple the fluid to an Aristotelian background [43,44] rather than a conventional Lorentzian spacetime manifold, here we will find it desirable to "generalize" the Aristotelian background to an even more generic family of geometries which does not demand any accidental symmetry. The natural conclusion is that one should couple the fluid with only discrete rotational symmetry directly to the vielbein.…”

“…Let us start by considering the example of the non-boost invariant system, but with otherwise the full rotational symmetry group O(d). Here, the underlying geometry is the Aristotelian geometry [43,44]. The temporal vielbein e 0 µ is independent as there is no boost symmetry relating it to the spatial ones; while the spatial vielbeins are required to form a "metric" h µν , which is a rank-d (d + 1) × (d + 1) symmetric tensor.…”

Fractons in curved space

“…We are interested in physical systems that are invariant under spacetime translations and spatial rotations, but with no boost symmetry -Galilean or Lorentz. Such systems naturally couple to the so-called Aristotelian background 2 sources [28][29][30]. 3 The sources consist of a clock-form n µ and a degenerate symmetric spatial metric tensor h µν .…”

“…From there, it is straightforward to generalise the methods of [21][22][23][24][25] (as well as e.g. [26][27][28][29][30] on constructing theories of transport in the non-relativistic setting) to obtain the dissipative hydrodynamic description of these models, either from the point of view of constitutive relations and conservation equations, or from the point of view of a Keldysh effective field theory.…”

Enstrophy without boost symmetry

“…The dynamics of such fluids is of interest due to its proximity to the dynamics of flocking behavior [6]. Also, by an appropriate enhancement of symmetries, the non frame invariant fluid equations of motion transform into a variety of boost invariant or Lifshitz invariant fluid equations of motion [7][8][9][10].…”