Path Integral Evaluation of Non-Abelian Anomaly and Pauli--Villars--Gupta Regularization

TL;DR

This paper clarifies the relationship between different regularization schemes in path integral evaluations of non-Abelian anomalies, specifically linking the Pauli--Villars--Gupta regularization to consistent and covariant anomaly forms.

Contribution

It establishes a clear connection between PVG regularization and the gauge anomaly regularization schemes, including a reformulation at the Lagrangian level.

Findings

Conventional PVG corresponds to the consistent anomaly scheme.

Generalized PVG realizes the covariant anomaly scheme.

Reformulation as regularization of the gauge current operator clarifies the scheme relations.

Abstract

When the path integral method of anomaly evaluation is applied to chiral gauge theories, two different types of gauge anomaly, i.e., the consistent form and the covariant form, appear depending on the regularization scheme for the Jacobian factor. We clarify the relation between the regularization scheme and the Pauli--Villars--Gupta (PVG) type Lagrangian level regularization. The conventional PVG, being non-gauge invariant for chiral gauge theories, in general corresponds to the consistent regularization scheme. The covariant regularization scheme, on the other hand, is realized by the generalized PVG Lagrangian recently proposed by Frolov and Slavnov. These correspondences are clarified by reformulating the PVG method as a regularization of the composite gauge current operator.