The metaphysics of fibre bundles

Recently, Dewar (2019) has suggested that one can apply the strategy of 'sophistication'-as exemplified by sophisticated substantivalism as a response to the diffeomorphism invariance of General Relativity-to gauge theories such as electrodynamics. This requires a shift to the formalism of fibre bundles. In this paper, I develop and defend this suggestion. Where my approach differs from previous discussions is that I focus on the metaphysical picture underlying the fibre bundle formalism. In particular, I aim to affirm the physical reality of gauge properties. I argue that this allows for a local and separable explanation of the Aharonov-Bohm effect. Its puzzling features are explained by a form of holism inherent to fibre bundles.