Alexander Sahakian, USC

Abstract: In physics, a gauge theory describes fields on spacetime which admit potentials invariant under the pointwise action of some Lie group. Mathematically, the potentials in a gauge theory are modeled by connection 1-forms on principal bundles over spacetime, with the physically measurable field strengths being defined by their curvature. A particle propagating in the presence of a gauge field experiences a force coming from the coupling of the potential to its 1-dimensional trajectory; in differential geometric terms, this is measured by parallel transport over that trajectory. In string theory and M-theory, as one replaces particles by higher dimensional extended objects, the appropriate potentials which couple to the trajectories of these objects are described locally by higher order forms, and globally by connective structures on higher order gerbes. In Section 1, we'll begin with a quick introduction to classical field theory, and in Section 2, we'll continue with an introduction to ordinary gauge theory. Lastly in Section 3, we'll generalize to the setting of string theory and M-theory, and see how it gives rise to higher gauge theory and the differential geometry of gerbes.