Chiral anomaly

The chiral anomaly is the quantum nonconservation of a classically conserved axial current in a gauge-field background.

For massless Dirac fermions, the classical axial current is $J_A^{\mu }=\bar{\psi }{\gamma }^{\mu }{\gamma }^5\psi$. The chiral anomaly makes its divergence proportional to $F_{\mu \nu }{}^{\star }{F}^{\mu \nu }$.