Callan-Rubakov Effect and Higher Charge Monopoles

Abstract: In this paper we study the interaction between magnetic monopoles and massless fermions. In the low energy limit, the monopole's magnetic field polarizes the fermions into purely in-going and out-going modes. Unitarity requires that the UV fermion-monopole interaction leads to non-trivial IR boundary conditions that relate the in-going to out-going modes. These non-trivial boundary conditions lead to what is known as the Callan-Rubakov effect. Here we derive the effective boundary condition by explicitly integrating out the UV degrees of freedom for the general class of spherically symmetric $SU(N)$ monopoles coupled to massless fermions of arbitrary representation. We then show that the boundary conditions preserve continuous symmetries without ABJ-type anomalies. As an application we explicitly derive the boundary conditions for the stable, spherically symmetric monopoles associated to the $SU(5)$ Georgi-Glashow model and comment on the relation to baryon number violation.