Title: Stable Excited Dyonic States of Magnetic Monopoles
Abstract: Advancements in our understanding of new physics can be largely divided into two areas of study: phenomenology and theory with the former concerning the formulation of new theories and holding them to scrutiny against experimental evidence while the latter involves the in-depth study of these theories to better understand the scope of their implications. To reflect this dichotomy, this thesis is broken into two acts: one covering progress made on the phenomenological front and the other covering progress made on the theoretical front. This defense will focus on the latter by detailing advancements made in our understanding of the structure of magnetic monopoles. In the mid-1970's, t'Hooft and Polyakov discovered magnetic monopoles exist as generic solutions in spontaneously broken gauge theories. Since then much progress has been made in understanding these monopoles, most notably by Callan who argued that the fermion vacuum is non-trivial around a magnetic monopole and can be interpreted as bound states of fermions with fractional fermion number. In this work, we explicitly compute these fermion bound states in an SU(2) gauge theory coupled to Nf  fermions. We demonstrate there are two unique ways to grant mass to the fermions in the SU(2) theory which, after symmetry breaking, both give a theory of QED with Nf massive fermions. Despite this seeming equivalence of the two theories at low energies, we demonstrate that the structure of the fermion bound states differ drastically between them and as a consequence can encode information about the high-energy theory, which is accessible at low-energy scales. We find that each theory exhibits a different number of stable excited dyonic states of the monopole with differing charges and energies. We find the ground states can also differ in energy and charge between the two theories. We demonstrate the monopole can inherit a mass correction and charge distribution that depends on the topological  angle even if one of the fermions is massless. This effect is present in one of the theories and is completely absent in the other. Finally, we discuss the implications of these effects on the SU(5) GUT monopole.