Anomalous hydrodynamics with triangular point group in 2+1 dimensions

We present a theory of hydrodynamics for a vector U(1) charge in $2+1$ dimensions, whose rotational symmetry is broken to the point group of an equilateral triangle. We show that it is possible for this U(1) to have a chiral anomaly. The hydrodynamic consequence of this anomaly is the introduction of a ballistic contribution to the dispersion relation for the hydrodynamic modes. We simulate classical Markov chains and find compelling numerical evidence for the anomalous hydrodynamic universality class. Generalizations of our theory to other symmetry groups are also discussed.