Anomalies and chiral symmetry in QCD

Michael Creutz

Published 2008-12-31, updated 2009-01-27Version 2

I review some aspects of the interplay between anomalies and chiral symmetry. The quantum anomaly that breaks the U(1) axial symmetry of massless QCD leaves behind a flavor-singlet discrete chiral invariance. When the mass is turned on this residual symmetry has a close connection with the strong CP violating parameter theta. One result is that a first order transition is usually expected when the strong CP violating angle passes through pi. This symmetry can be understood either in terms of effective chiral Lagrangians or in terms of the underlying quark fields.