Lattice Weyl Fermion on a Single Spherical Domain-Wall

TL;DR

This paper explores the emergence and localization of Weyl fermions on a spherical domain-wall in a 3D lattice, revealing how gauge potentials and monopoles influence zero modes and chirality.

Contribution

It demonstrates the realization of Weyl fermions on a spherical domain-wall using lattice fermion formulation and analyzes the effects of gauge fields and monopoles on zero modes.

Findings

Weyl fermions localize on the spherical domain-wall.

Presence of gauge potential introduces additional zero modes.

Monopoles induce centrally localized zero modes.

Abstract

We investigate a single spherical domain-wall embedded in a three-dimensional Euclidean lattice. We employ the Shamir-type domain-wall fermion formulation, where the negative mass region is confined inside the $S^2$ domain-wall, while the positive mass outside is taken to the infinite limit, allowing the exterior region to be neglected effectively. In the absence of a gauge potential, Weyl fermions emerge as edge-localized modes along the $S^2$ domain-wall. When a nontrivial $U(1)$ gauge potential is present, additional zero modes with opposite chirality appears, localized at the center near the monopole. This centrally localized mode originates from the effective mass contribution of the Wilson term, which induces a domain-wall near the monopole.