Infinitely many regulator fields for chiral fermions

TL;DR

This paper unifies two recent methods for regularizing chiral gauge theories by introducing an infinite number of regulator fields, providing a potentially all-orders perturbative approach and a lattice implementation.

Contribution

It reveals a common underlying trick behind two regularization proposals and introduces a Pauli-Villars and lattice realization for chiral fermion regularization.

Findings

Unified regularization framework for chiral fermions.

Proposed a lattice version consistent with continuum limits.

Potential for all-orders perturbative consistency.

Abstract

We show that two recent independent proposals for regularizing a chiral gauge theory stem from one common trick. If the anomaly free complex representation carried by the right handed fermi--fields is $r$ one constructs a vector like theory with flavored right handed fermionic matter in $r+\bar r$ but with a mass matrix of the order of the cutoff and having an index equal to unity in an infinite dimensional flavor space. We present a Pauli--Villars realization of the trick that is likely to work to all orders in perturbation theory and a lattice version which is argued to produce the correct continuum leading order fermionic contribution to the vacuum polarization tensor and readied for further perturbative checks.