Vortex fermion on the lattice

TL;DR

This paper introduces a new lattice regularization for vortex fermions in 4+2 dimensions, demonstrating the existence of a normalizable zero mode solution at the vortex core, advancing chiral fermion realization on the lattice.

Contribution

It constructs vortex fermions on the lattice via a novel 4+2 dimensional reduction with a discrete rotational invariant regularization, including an extended Wilson term to eliminate doublers.

Findings

Normalizable zero mode appears at vortex core

New lattice regularization with discrete rotational invariance

Extended Wilson term effectively removes doublers

Abstract

The domain wall fermion formalism in lattice gauge theory is much investigated recently. This is set up by reducing 4+1 dimensional theory to low energy effective 4 dimensional one. In order to look around other possibilities of realizing chiral fermion on the lattice, we construct vortex fermion by reducing 4+2 dimensional theory to low energy effective 4 dimensional one on the lattice. In extra 2 dimensions we propose a new lattice regularization which has a discrete rotational invariance but not a translational one. In order to eliminate doubling species in the naive construction we introduce the extended Wilson term which is appropriate to our model. We propose two models for convenience and show that a normalizable zero mode solution appears at the core of the vortex.