Fermion zero modes in a $Z_2$ vortex background

TL;DR

This paper investigates fermion zero energy solutions in a non-Abelian gauge model with a $Z_2$ vortex, explicitly deriving zero modes for specific configurations to understand their properties.

Contribution

It provides explicit forms and counts of fermionic zero modes in a non-Abelian gauge background with a $Z_2$ vortex, advancing understanding of fermion-vortex interactions.

Findings

Explicit fermion zero modes derived for specific vortex configurations

Number of zero modes determined in the $Z_2$ vortex background

Enhanced understanding of fermion behavior in non-Abelian gauge fields

Abstract

In this paper we study the zero energy solutions of the Dirac equation in the background of a $Z_2$ vortex of a non-Abelian gauge model with three charged scalar fields. We determine the number of the fermionic zero modes giving their explicit form for two specific Ansatze.