Gauge Invariant Pauli-Villars Regularization of Chiral Fermions

TL;DR

This paper develops a gauge invariant regularization scheme for chiral fermions using an extended Pauli-Villars method, ensuring anomaly-free conditions and gauge invariance in various representations.

Contribution

It generalizes the Pauli-Villars regularization to chiral fermions, providing a gauge invariant scheme applicable to arbitrary anomaly-free representations.

Findings

Vacuum polarization tensor is transverse.

Fermion number and conformal anomalies are gauge invariant.

Scheme is straightforward for real representations.

Abstract

We extend the idea of the generalized Pauli-Villars regularization of Frolov and Slavnov and analyze the general structure of the regularization scheme. The gauge anomaly-free condition emerges in a simple way in the scheme, and, under the standard prescription for the momentum assignment, the Pauli-Villars Lagrangian provides a gauge invariant regularization of chiral fermions in arbitrary anomaly-free representations. The vacuum polarization tensor is transverse, and the fermion number and the conformal anomalies have gauge invariant forms. We also point out that the real representation can be treated in a straightforward manner and the covariant regularization scheme is directly implemented.