Chiral anomaly

The chiral anomaly is the quantum nonconservation of a classically conserved axial current. For massless charged Dirac fields, the classical axial rotation is a symmetry, but a quantization preserving the vector gauge symmetry gives an axial-current divergence proportional to $F_{\mu \nu }{}^{\star }{F}^{\mu \nu }$.

This is a physical effect: the electromagnetic chiral anomaly helps determine the neutral pion's decay amplitude into two photons. A global axial symmetry may fail in this way while the gauge theory remains consistent. A gauge anomaly is different because the lost gauge redundancy is needed to remove unphysical states.^[ref]