Anomalies and chiral symmetry in QCD

TL;DR

This paper reviews the relationship between quantum anomalies and chiral symmetry in QCD, highlighting how anomalies influence phase transitions and residual symmetries, with implications for the strong CP problem.

Contribution

It clarifies the connection between anomalies, chiral symmetry, and the strong CP parameter using both effective theories and fundamental quark descriptions.

Findings

Anomaly breaks U(1) axial symmetry but leaves a discrete chiral invariance.

A first order transition is expected at theta = pi.

Residual symmetry relates to the strong CP violating parameter.

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.