An exploration of the strong coupling regime of the su(2) georgi-glashow model

Abstract

In this dissertation, we delve into an in-depth analysis of the $SU(2)$ Georgi-Glashow model in a four-dimensional space-time configuration, particularly emphasizing its strong coupling behavior. We systematically investigate several order parameters inherent to the model, unveiling hitherto unobserved critical phenomena within a distinct parameter range. Notably, the model has interesting topological phenomena such as monopoles. The scaling behavior of the model is juxtaposed with the pure $SU(2)$ model. Furthermore, we illuminate the phase diagram that illustrates the relationship between the magnitude of Higgs and center symmetry breaking. Our analysis reveals an interesting overlap between these phase transitions across an expansive portion of the strong coupling regime, establishing an unexpected correlation between two unrelated phase transitions. Complementing this, we extend our investigation to the $3$-dimensional $N=4$ supersymmetric Yang-Mills model, identifying minimal $Q$-closed terms and establishing that the low-level Feynman integrals are $0$. Studying this contributes to our long-term understanding of the Montonen-Olive duality in supersymmetric Yang-Mills.