Unpaired Weyl fermion on an axion string in a finite lattice

TL;DR

This paper demonstrates a lattice construction of a single unpaired Weyl fermion using a string defect in a higher-dimensional spacetime, with implications for chiral gauge theories and axion cosmology.

Contribution

It introduces a lattice model of an axion string defect in (2+2) dimensions to realize a Weyl fermion, extending previous domain wall fermion approaches.

Findings

Realizes a Weyl fermion on a finite lattice using a string defect.

Uses a Hamiltonian formulation in Minkowski spacetime.

Framework applicable to lattice chiral gauge theories and axion cosmology.

Abstract

Domain wall fermions use a $2n$-dimensional spacetime defect embedded in $(2n+1)$-dimensional spacetime to realize massless lattice Dirac fermions. Recent work has extended this idea to realize a single unpaired Weyl fermion in a finite lattice. Here, we realize the same using a $2n$-dimensional string defect embedded in $(2n+2)$-dimensional spacetime on a finite lattice for $n=1$. This string is a lattice version of the continuum axion string described in Callan-Harvey. Our results are obtained in a Hamiltonian formulation in Minkowski spacetime. Extending the results to Euclidean spacetime and to $n>1$ is straightforward. This work has applications to lattice chiral gauge theories and axion cosmology.