A novel regularization of chiral gauge theory

TL;DR

This paper introduces a new gauge-invariant regularization method for perturbative chiral gauge theories, combining domain-wall fermions with dimensional regularization of gauge fields, ensuring correct anomaly reproduction and automatic renormalization.

Contribution

It presents a novel regularization scheme at the Lagrangian level that preserves gauge invariance and correctly reproduces anomalies in chiral gauge theories.

Findings

Correctly reproduces Abelian anomaly

Achieves automatic renormalization with counter terms

Implemented directly at the Lagrangian level

Abstract

We propose a novel gauge-invariant regularization for the perturbative chiral gauge theory.Our method consists of the two ingredients: use of the domain-wall fermion to describe a chiral fermion with Pauli-Villars regulators and application of the di- mensional regularization only to the gauge field. This regularization is implemented in the Lagrangian level, unlike other gauge-invariant regularizations (eg. the covariant regularizations). We show that the Abelian (fermion number) anomaly is reproduced correctly in this formulation. We also show that once we add the counter terms to the full theory, then the renormalization in the chiral gauge theory is automatically achieved.