Fermions localized on $U(1)$ gauged Q-balls

TL;DR

This paper demonstrates that fermions can form normalizable bound states on $U(1)$ gauged Q-balls with minimal electromagnetic coupling, exploring their existence, properties, and the negligible backreaction effects.

Contribution

It introduces the existence of fermionic bound states on $U(1)$ gauged Q-balls and analyzes their physical properties and stability.

Findings

Fermionic bound states exist on gauged Q-balls.

Backreaction effects of fermions are minimal.

No zero modes are present in the spectrum.

Abstract

The axially symmetric $U(1)$ gauged self-interacting Q-balls are shown to support normalizable fermionic bound state, minimally coupled to the electromagnetic field of the Q-ball. It is shown that the effects of the backreaction of the fermionic mode are very small. We explore the domain of existence of the solutions and address some of their physical properties. Among other properties, we observe that the eigenvalue of the Dirac operator remains positive, there is no zero mode in the spectrum.