Lectures on Higher Gauge Theory

From CRCG-Wiki

Gauge theory describes the parallel transport of point particles using the formalism of connections on bundles. In both string theory and loop quantum gravity, point particles are replaced by 1-dimensional extended objects: paths or loops in space. This suggests that we seek some sort of "higher gauge theory" that describes parallel transport as we move a path through space, tracing out a surface. To find the right mathematical language for this, we must "categorify" concepts from topology and geometry, replacing smooth manifolds by smooth categories, Lie groups by Lie 2-groups, Lie algebras by Lie 2-algebras, bundles by 2-bundles, sheaves by stacks or gerbes, and so on. This overview of higher gauge theory will emphasize its relation to homotopy theory and the cohomology of groups and Lie algebras.

You can see the lectures and further reading material on my website.

• Lecture 1- Lie 2-groups and Lie 2-algebras. 2-3 pm, Thursday February 5th.

• Lecture 2 - 2-bundles and classifying spaces for 2-groups. 9-10 am, Friday February 6th.

• Lecture 3 - 2-connections on 2-bundles. 3-4 pm, Friday February 6th.