More chiral operators on the lattice

TL;DR

This paper introduces a broader class of lattice Dirac operators satisfying generalized chiral symmetry, expanding beyond Ginsparg-Wilson fermions, and demonstrates their suitability for describing Weyl fermions and chiral gauge theories.

Contribution

It proposes a larger class of chiral lattice Dirac operators based on generalized chiral symmetry, extending previous formulations like GW fermions.

Findings

The index depends only on a basic unitary operator.

Spectral analysis reveals detailed properties of the new operators.

Weaker conditions still produce proper Weyl fermions and chiral gauge theories.

Abstract

Instead of the Ginsparg-Wilson (GW) relation we only require generalized chiral symmetry and show that this results in a larger class of Dirac operators describing massless fermions, which in addition to GW fermions and to the ones proposed by Fujikawa includes many more general ones. The index turns out to depend solely on a basic unitary operator. We use spectral representations to analyze the new class and to obtain detailed properties. We also show that our weaker conditions still lead properly to Weyl fermions and to chiral gauge theories.