Magnetic monopoles and dyons: The low-energy perspective

Abstract

This thesis uses the framework of point-particle effective field theory (PPEFT) to describe the interactions of magnetic monopoles and dyons with low-energy relativistic fermions. Our main goal in doing so is to reconcile the apparent inconsistency between the decoupling principle – which states that short-distance physics decouples from long-distance observables – and the famous observation that monopole-fermion (or dyon-fermion) scattering need not be suppressed by the heavy monopole or dyon mass. We further use this effective field theory description to explore the long-distance complications associated with polarizing the fermionic vacuum exterior to a dyon and show in some circumstances how our methods can simplify calculations of low-energy fermion-dyon scattering in their presence. We propose an effective Hamiltonian governing how dyon excitations respond to fermion scattering in terms of a time-dependent vacuum angle and outline open questions remaining in its microscopic derivation. Although we predominantly focus on the simplest examples of monopole and dyon solutions, our methods lay the foundation for describing how more realistic monopoles and dyons – those arising in Grand Unified Theories – couple to Standard Model fields.