Differential Geometry Working Seminar | Danial Ghamari | Higher Gauge Theory

Ordinary gauge theory describes the parallel transport of point particles along paths using connections on principal bundles. Higher gauge theory extends this framework to objects such as strings, whose motion sweeps out surfaces. This extension requires a corresponding categorification. As long as time permits, we will go through Baez and Schreiber (2006), Higher Gauge Theory, and develop the main ideas presented there. In particular, we will explain how Lie groups, bundles, and connections are replaced by Lie 2-groups, principal 2-bundles, and 2-connections. We will motivate this structure through surface holonomy and the obstruction to describing nonabelian surface transport using ordinary groups. We will then outline the construction of path and surface holonomy as a 2-functor, the local description of a 2-connection by differential forms (A) and (B), and its relation to nonabelian gerbes. Time permitting, we will discuss why parametrization-independent surface transport requires the vanishing of the fake curvature. In the likely case that we do not manage to cover the entire paper, we will have follow-up talks in which we continue developing the theory.

MC 5417