A Perturbative Construction of Lattice Chiral Fermions

TL;DR

This paper introduces a perturbative method to construct lattice chiral fermions that respects chiral symmetry and reproduces continuum anomalies, demonstrating a viable lattice regularization.

Contribution

It presents a novel perturbative approach to derive a chirally invariant effective action for lattice fermions, consistent with the Nielsen-Ninomiya theorem.

Findings

Effective lattice action is nonlocal and chirally invariant.

The axial anomaly is correctly reproduced in the Schwinger model.

Chiral fermions can be regularized on the lattice using this method.

Abstract

We perform a renormalization group transformation to construct a lattice theory of chiral fermions. The field variables of the continuum theory are averaged over hypercubes to define lattice fields. Integrating out the continuum variables in perturbation theory we derive a chirally invariant effective action for the lattice fields. This is consistent with the Nielsen-Niniomiya theorem because the effective action is nonlocal. We also construct the axial current on the lattice and we show that the axial anomaly of the continuum theory is reproduced in the Schwinger model. This shows that chiral fermions can be regularized on the lattice.