On the conservation of electric charge around a monopole of finite size

Abstract

In monopole-fermion dynamics, the boundary condition which is responsible for baryon number non-conservation also violates electric and color hypercharge conservation. We show by detailed calculations that actually the latter conservation laws are dynamically restored. It is shown that for a finite size monopole, there is a small but finite amplitude for the monopole ground state to make a virtual transition into a state containing a dyon and some fermions carrying equal and opposite charge as that of the dyon. But the amplitude for this state to make a virtual transition to a state carrying a net total charge is identically zero. The monopole ground state, as a result, is an eigenstate of electric charge even in the presence of massless fermions. We also calculate the four-body charge and chirality conserving but baryon number violating condensates, which exist independently of the existence of the anomaly and hence persist even in the presence of more generations of massless fermions.