On consistency of hydrodynamic approximation for chiral media

We consider chiral liquids, that is liquids consisting of massless fermions and right–left asymmetric. In such media, one expects existence of electromagnetic current flowing along an external magnetic field, associated with the chiral anomaly. The current is predicted to be dissipation-free. We consider dynamics of chiral liquids, concentrating on the issues of possible instabilities and infrared sensitivity. Instabilities arise, generally speaking, already in the limit of vanishing electromagnetic constant, αel→ 0αel→ 0. In particular, liquids with non-vanishing chiral chemical potential might decay into right–left asymmetric states containing vortices.