Abstract: Axial-current anomaly is the fundamental property of quantum field theory with Dirac fermions coupled to a vector gauge field. In quantum electrodynamics, for example, the anomaly states that the divergence of the axial current does not vanish as it would follow from the classical Dirac equation but is controlled by the electromagnetic field.
Recently and quite remarkably the axial-current anomaly has been identified in the hydrodynamic of a classical ideal fluid as a kinematic property of the Euler equation. In fluid, the axial current is closely related to the fluid helicity and (in appropriate units) is identical to that of the axial current of quantum Dirac fermions in QED. The talk is based on the joint works with A. Abanov.
