  We develop the formalism that incorporates quantum anomalies in the effective
field theory of non-dissipative fluids. We consider the effect of adding a
Wess-Zumino-like term to the low-energy effective action to account for
anomalies. In this paper we restrict to two spacetime dimensions. We find
modifications to the constitutive relations for the current and the
stress-energy tensor, and, more interestingly, half a new propagating mode
(one-and-a-halfth sound): a left- or right-moving wave with propagation speed
that goes to zero with the anomaly coefficient. Unlike for the chiral magnetic
wave in four dimensions, this mode propagates even in the absence of external
fields. We check our results against a more standard, purely hydrodynamical
derivation. Unitarity of the effective field theory suggests an upper bound on
the anomaly coefficient in hydrodynamics.
