Fermions localized on U(1) gauged Q-balls

The axially symmetric U (1) gauged self-interacting Q-balls are shown to support normalizable fermionic bound states, 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 in the range of the system parameters studied. We explore the domain of existence of the solutions and address some of their physical properties. Among other properties, we observe that, for the bound mode, the eigenvalue of the Dirac operator remains positive, there is no zero mode in the spectrum, as expected in a theory with finite bare fermionic mass in the absence of the Yukawa coupling.