Anomalies and chiral symmetry in QCD

Abstract

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.

19 pages, 12 figures. Revision adds references and corrects minor typos

References in corpus (3)

• Spontaneous CP-violation in the strong interaction at theta = pi
• One flavor QCD
• The 't Hooft vertex revisited

Cited by in corpus (10)

• Polyakov loop modeling for hot QCD
• Electric-current Susceptibility and the Chiral Magnetic Effect
• Vacuum structure of bifundamental gauge theories at finite topological angles
• Global inconsistency, 't Hooft anomaly, and level crossing in quantum mechanics
• The chiral phase transition and the axial anomaly
• Deconfinement and CP-breaking at $\theta =\pi$ in Yang-Mills theories and a novel phase for SU(2)
• Quark mass dependence of two-flavor QCD
• QCD $\theta$-vacua from the chiral limit to the quenched limit
• $U_A(1)$ symmetry breaking quark interactions from vacuum polarization
• First-order CP phase transition in two-flavor QCD at $\theta =\pi$ under electromagnetic scale anomaly via a Nambu-Jona-Lasinio description