Remark on Pauli-Villars Lagrangian on the Lattice

TL;DR

This paper explores combining Pauli-Villars regularization with lattice regularization, demonstrating how it corrects gauge non-invariance in axial anomaly calculations using a simple fermion model.

Contribution

It shows how Pauli-Villars regularization can be applied on the lattice to address gauge invariance issues in axial anomaly computations, including a discussion on regulators for anomaly-free models.

Findings

Gauge non-invariance caused by Wilson term is compensated in the continuum limit.

Pauli-Villars regulators restore gauge invariance in lattice axial anomaly calculations.

Brief mention of regulators needed for anomaly-free chiral fermions in Frolov-Slavnov scheme.

Abstract

It is interesting to superimpose the Pauli-Villars regularization on the lattice regularization. We illustrate how this scheme works by evaluating the axial anomaly in a simple lattice fermion model, the Pauli-Villars Lagrangian with a gauge non-invariant Wilson term. The gauge non-invariance of the axial anomaly, caused by the Wilson term, is remedied by a compensation among Pauli-Villars regulators in the continuum limit. A subtlety in Frolov-Slavnov's scheme for an odd number of chiral fermions in an anomaly free complex gauge representation, which requires an infinite number of regulators, is briefly mentioned.