Generalizing emergent gauge theories to non-abelian settings and exploring emergence in geometrical underpinnings using fiber bundles

Abstract

Attempts to devise a quantum theory of gravity consistent with the standard model have so far been unsuccessful; however, it is widely agreed that gravity can be described as a non-abelian gauge theory, and that the particle mediating the gravitational force (the graviton) would be a spin-2 boson. Under certain circumstances it is possible for gauge symmetries to emerge from theories containing only physical symmetries. It can also be shown that the gauge theories characteristic of the standard model are low energy approximations emerging from more fundamental principles\cite{witten}. While it is true that the Weinberg-Witten theorem excludes a large class of emergent theories from describing gravitation\cite{WW}, it has been shown that non-abelian theories can be formulated such that the Weinberg-Witten theorem does not apply. Currently, this result has only been shown using a functional formalism. The standard model has been described using both functional and a geometrical interpretations. The geometrical interpretation involves describing gauge transformations as connections on principal bundles\cite{weatherall}. The purpose of this thesis is to form a geometrical description of non-abelian emergent gauge theories using a fiber bundle formalism.