Hydrodynamic effective field theories with discrete rotational symmetry

We develop a hydrodynamic effective field theory on the Schwinger-Keldysh contour for fluids with charge, energy, and momentum conservation, but only discrete rotational symmetry. The consequences of anisotropy on thermodynamics and first-order dissipative hydrodynamics are detailed in some simple examples in two spatial dimensions, but our construction extends to any spatial dimension and any rotation group (discrete or continuous). We find many possible terms in the equations of motion which are compatible with the existence of an entropy current, but not with the ability to couple the fluid to background gauge fields and vielbein.

Automated summary

This paper develops a hydrodynamic effective field theory on the Schwinger-Keldysh contour for fluids with conservation of charge, energy, and momentum, but with only discrete rotational symmetry. The effects of anisotropy on thermodynamics and first-order dissipative hydrodynamics are explained through simple examples in two spatial dimensions, although the theory can be extended to any number of spatial dimensions and any rotation group (discrete or continuous). The study uncovers several possible terms in the equations of motion that are compatible with the existence of an entropy current, but not with the ability to couple the fluid to background gauge fields and vielbein.