Generalized Pauli-Villars Regularization and the Covariant Form of Anomalies

TL;DR

This paper clarifies how the generalized Pauli-Villars regularization reproduces covariant anomalies in chiral gauge theories by reformulating it as a regularization of composite current operators, highlighting its properties and implications.

Contribution

It demonstrates the connection between infinite regulator sums and covariant anomalies, providing a reformulation that explains the regularization's effects on anomalies and symmetries.

Findings

Reformulation of Pauli-Villars as current operator regularization

Reproduction of covariant fermion number anomaly in Weinberg-Salam theory

Covariant regularization preserves gauge invariance and Bose symmetry in anomaly-free theories

Abstract

In the generalized Pauli-Villars regularization of chiral gauge theory proposed by Frolov and Slavnov , it is important to specify how to sum the contributions from an infinite number of regulator fields. It is shown that an explicit sum of contributions from an infinite number of fields in anomaly-free gauge theory essentially results in a specific choice of regulator in the past formulation of covariant anomalies. We show this correspondence by reformulating the generalized Pauli- Villars regularization as a regularization of composite current operators. We thus naturally understand why the covariant fermion number anomaly in the Weinberg-Salam theory is reproduced in the generalized Pauli-Villars regularization. A salient feature of the covariant regularization,which is not implemented in the lagrangian level in general but works for any chiral theory and gives rise to covariant anomalies , is that it spoils the Bose symmetry in anomalous theory. The covariant regularization however preserves the Bose symmetry as well as gauge invariance in anomaly-free gauge theory.