Minimally doubled chiral fermions with C, P and T symmetry on the staggered lattice

TL;DR

This paper introduces a new local lattice action for chiral fermions that preserves key symmetries and minimizes fermion doubling, inspired by graphene and reinterpretation of staggered lattice methods.

Contribution

A novel approach to construct local, symmetric lattice actions for chiral fermions with minimal doublers using a reinterpretation of staggered lattice techniques.

Findings

Constructed a local lattice action with all discrete symmetries

Achieved minimal fermion doubling in the lattice action

Demonstrated non-Hermitian but usable fermion action

Abstract

Recently, the interest in local lattice actions for chiral fermions has revived, with the proposition of new local actions in which only the minimal number of doublers appear. The trigger role of graphene having a minimally doubled, chirally invariant, Dirac-like excitation spectrum can not be neglected. The challenge is to construct an action which preserves enough symmetries to be useful in lattice gauge calculations. We present a new approach to obtain local lattice actions for fermions using a reinterpretation of the staggered lattice approach of Kogut and Susskind. This interpretation is based on the similarity with the staggered lattice approach in FDTD simulations of acoustics and electromagnetism. It allows us to construct a local action for chiral fermions which has all discrete symmetries and the minimal number of fermion flavors, but which is non-Hermitian in real space. However, we argue that this will not pose a threat to the usability of the theory.