Manifestly Gauge Covariant Treatment of Lattice Chiral Fermion

TL;DR

This paper introduces a lattice formulation for chiral fermions that preserves gauge symmetry and eliminates species doublers by using a novel approach based on the fermion propagator and gauge current operators.

Contribution

It presents a gauge covariant lattice formulation of chiral fermions that avoids species doubling without relying on the traditional fermion action.

Findings

Confirmed gauge covariance through perturbative tests

Demonstrated absence of fermion doublers

Applicable to numerical simulations in quenched approximation

Abstract

We propose a lattice formulation of the chiral fermion which maximally respects the gauge symmetry and simultaneously is free of the unwanted species doublers. The formulation is based on the lattice fermion propagator and composite operators, rather than on the lattice fermion action. The fermionic determinant is defined as a functional integral of an expectation value of the gauge current operator with respect to the background gauge field: The gauge anomaly is characterized as the non-integrability. We perform some perturbative test to confirm the gauge covariance and an absence of the doublers. The formulation can be applied rather straightforwardly to numerical simulations in the quenched approximation.