Pauli-Villars regularization of non-Abelian gauge theories

TL;DR

This paper develops a BRST-invariant regularization scheme for non-Abelian gauge theories using Pauli-Villars fields, aiming to facilitate nonperturbative solutions of light-front QCD.

Contribution

It extends PV regularization to SU(N) Yang-Mills theories with matter, incorporating BRST symmetry and auxiliary scalars for mass generation.

Findings

Constructed a BRST-invariant Lagrangian with PV fields

Generalized gauge symmetry for PV gluons

Potential foundation for nonperturbative light-front QCD

Abstract

As an extension of earlier work on QED, we construct a BRST-invariant Lagrangian for SU(N) Yang-Mills theory with fundamental matter, regulated by the inclusion of massive Pauli-Villars (PV) gluons and PV quarks. The underlying gauge symmetry for massless PV gluons is generalized to accommodate the PV-index-changing currents that are required by the regularization. Auxiliary adjoint scalars are used, in a mechanism due to Stueckelberg, to attribute mass to the PV gluons and the PV quarks. The addition of Faddeev--Popov ghosts then establishes a residual BRST symmetry. Although there are drawbacks to the approach, in particular the computational load of a large number of PV fields and a nonlocal interaction of the ghost fields, this formulation could provide a foundation for renormalizable nonperturbative solutions of light-front QCD in an arbitrary covariant gauge.