Fermionic Zero Modes in Gauge and Gravity Backgrounds on a Sphere

TL;DR

This paper investigates the existence of normalizable fermionic zero modes in gauge and gravity backgrounds on a two-dimensional sphere, revealing conditions under which massless Dirac fermions can arise in such compactified models.

Contribution

It demonstrates the presence of normalizable fermionic zero modes on a sphere in gauge and gravity backgrounds, providing explicit examples and broad conditions for their existence.

Findings

Massless Dirac fermions with zero modes exist on $S^2$

Zero modes are normalizable under general background assumptions

Explicit solutions for special gauge backgrounds are obtained

Abstract

In this letter we study fermionic zero modes in gauge and gravity backgrounds taking a two dimensional compact manifold $S^2$ as extra dimensions. The result is that there exist massless Dirac fermions which have normalizable zero modes under quite general assumptions about these backgrounds on the bulk. Several special cases of gauge background on the sphere are discussed and some simple fermionic zero modes are obtained.