Classification of Minimally Doubled Fermions

TL;DR

This paper introduces the Twisted-ordering Method to control fermion species in lattice QCD, leading to new minimally doubled actions with exact chiral symmetry and locality.

Contribution

It presents a novel method for controlling fermion species, expanding the class of minimally doubled lattice fermions with desirable symmetry and locality properties.

Findings

Developed the Twisted-ordering Method for fermion control

Constructed new minimally doubled fermion actions

Classified known minimally doubled fermions into two types

Abstract

We propose a method to control the number of species of lattice fermions which yields new classes of minimally doubled lattice fermions. We show it is possible to control the number of species by handling $O(a)$ Wilson-term-like corrections in fermion actions, which we will term ``Twisted-ordering Method". Using this method we obtain new minimally doubled actions with one exact chiral symmetry and exact locality. We classify the known minimally doubled fermions into two types based on the locations of the propagator poles in the Brillouin zone.