It is common for quantum field theories to lack a consistent, perturbative treatment. In most cases, this is because the couplings flow to a strongly-coupled regime, and the perturbative series diverges at all orders in these regimes. In some cases, such as those we will investigate for magnetic monopoles, the dynamics are inherently nonperturbative. In three dimensions, monopoles play the role of instantons and induce important corrections to the theory which are absent in a naive perturbative expansion around the trivial vacuum. In four dimensions, they appear as charged states, and the scattering processes involving electric and magnetic states fail to converge at any order in perturbation theory.

We begin by studying the conditions for fundamental zero modes of the Kaluza-Klein monopole which arises in compactified four dimensional theories. The existence of fundamental zero modes provide a path to decouple the Kaluza-Klein monopole in the zero radius limit such that the theory is purely three dimensional. We study the correspondence between the three and four dimensional theories under these effects.

Next, we study the moduli space for three dimensional supersymmetric SU(N) gauge theories with F

We now shift focus to an on-shell description of electric-magnetic scattering. Magnetically charged particles are theoretically well-motivated, but it is difficult to calculate the signatures of scattering events involving both magnetic and electrically charged particles. This cause for this difficulty is two-fold: there remains no local, Lorentz invariant Lagrangian description of such theories, and due to Dirac quantization, the coupling strength of the interactions are never weakly-coupled. We develop on-shell methods to study these processes, derive new selection rules, and calculate fermion-monopole scattering.

We end by changing gears and presenting a phenomenological study of dark matter freeze-out where the universe experiences an early QCD phase transition. Where dark matter freeze out is typically driven by annihilation into quarks, here the active degrees of freedom are mesons which alter the correspondence between the dark matter couplings to the Standard Model and the relic abundance of dark matter. We show that this model can explain the observed dark matter relic density while evading experimental constraints from direct detection.