Zero modes in vortex-fermion system with compact extra space

TL;DR

This paper demonstrates the existence of fermionic zero modes in a vortex-fermion system with a compact extra space, specifically on a manifold combining four-dimensional space and a two-sphere, linking higher-dimensional gauge configurations to known zero mode solutions.

Contribution

It shows the presence of fermionic zero modes in an $SU(2)$ gauge vortex system on a compactified manifold, connecting higher-dimensional gauge fields to four-dimensional effective theories.

Findings

Fermionic zero modes exist in the specified vortex configuration.

Zero modes resemble Jackiw-Rossi solutions in four dimensions.

Results bridge higher-dimensional gauge theories and effective four-dimensional models.

Abstract

The existence of fermionic zero modes is shown in the presence of vortex configuration of pure $SU(2)$ gauge field on the manifold $M_4 \times S^2$. From the perspective of four-dimensional effective theory, these zero modes are almost the same as the Jackiw-Rossi type zero modes of the vortex-fermion system.