Callan-Rubakov Effect and Higher Charge Monopoles

TL;DR

This paper derives effective boundary conditions for the Callan-Rubakov effect in higher charge monopoles, revealing how monopole-fermion interactions influence IR physics and symmetry preservation.

Contribution

It provides a general derivation of IR boundary conditions for spherically symmetric $SU(N)$ monopoles coupled to massless fermions, extending understanding of the Callan-Rubakov effect.

Findings

Derived explicit boundary conditions for $SU(5)$ monopoles.

Showed boundary conditions preserve continuous symmetries.

Connected boundary conditions to baryon number violation.

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.