On the anomalous superfluid hydrodynamics

It has been shown by Son and Surówka that the presence of anomaly in hydrodynamics with global U(1) symmetry can induce vortical and magnetic currents. The induced current is uniquely determined by anomaly from the existence of an entropy current with non-negative divergence. In this work, we extended the analysis to hydrodynamics with U(1) symmetry spontaneously broken, i.e. U(1) superfluid hydrodynamics. We found that all possible first order gradient corrections are determined up to one arbitrary function. Furthermore, the stress tensor does not receive correction from anomaly and the corrections to "Josephson" equation are fully determined by anomaly.