A New Solution to the Callan Rubakov Effect

TL;DR

This paper provides a comprehensive physical picture of monopole-fermion interactions in 4D SU(2) gauge theory, explaining charge transfer, dyon formation, and stability through a unified framework that resolves longstanding confusions in the Callan Rubakov effect.

Contribution

It introduces a complete, all-angular-momentum-inclusive model of monopole-fermion scattering, clarifying the formation and stability of dyons without adding new Hilbert space states.

Findings

Fermions excite trapped W-bosons, transforming monopoles into dyons.

Dyons acquire charge via a low-energy Witten effect and are stabilized by a $ ext{Z}_N$ symmetry.

Scattered fermions can form bound states with dyons, which decay into symmetric modes.

Abstract

In this paper we study the scattering of massive fermions off of smooth, spherically symmetric monopoles in $4d$ $SU(2)$ gauge theory. We propose a complete physical picture of the monopole-fermion interaction which encompasses all angular momentum modes. We show that as an in-going fermion scatters off a monopole, it excites trapped $W$-bosons in the monopole core by a version of the Witten effect so that the monopole can accrue charge and transform into a dyon at parametrically low energies. The imparted electric charge is then protected from decay by an emergent $\mathbb{Z}_N$ generalized global symmetry, creating a stable dyon. At sufficiently low energies, the scattered fermion can be trapped by the dyon's electrostatic potential, forming a bound state, which can decay into spherically symmetric fermion modes subject to the preserved $\mathbb{Z}_N$ global symmetry. We propose that monopole-fermion scattering can be described in this way without needing to add ``new'' states to the Hilbert space, thereby eliminating a long standing confusion in the Callan Rubakov effect.