Chiral Fermions and Anomalies on a Finite Lattice

TL;DR

This paper tests Kaplan's lattice chiral gauge theory proposal by calculating the spectrum, demonstrating chiral fermions, decoupling of doublers, and observing anomalies consistent with continuum theory on a finite lattice.

Contribution

It provides a numerical verification of chiral fermions and anomaly cancellation on a finite lattice, supporting Kaplan's approach.

Findings

Chiral fermions are successfully realized on the lattice.

Lattice doublers are shown to decouple.

Flavor anomalies match continuum anomaly relations.

Abstract

A recent proposal by Kaplan for a chiral gauge theory on the lattice is tested with background gauge fields. The spectrum of the finite lattice Hamiltonian is calculated and the existence of a chiral fermion is demonstrated. Lattice doublers are found to decouple. The flavor anomalies, which are in agreement with the continuum anomaly relation, are obeserved on a finite lattice. Non-trivial anomaly cancellation is observed in a chiral gauge current.