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Starting from a low energy effective chiral Lagrangian with a gauged Wess-Zumino-Witten term, we have derived a hydrodynamic theory for chiral superfluid. It is a non-Abelian hydrodynamics at zero temperature with only superfluid components. With an external electromagnetic field and baryonic and axial baryonic chemical potentials turned on, we are able to identify analogs of various anomaly induced terms in normal hydrodynamics, including a chiral vortical effect, a chiral magnetic effect, and a chiral electric effect. As an example, we solved the hydrodynamic equations for the ground state and observed the chiral magnetic effect and chiral separation in the confined phase.
Shu Lin (Fri,) studied this question.