John Baez

2006 Barrett Lectures

April 29-May 1, 2006

Higher Gauge Theory

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. We give an overview of higher gauge theory, with an emphasis on its relation to homotopy theory and the cohomology of groups and Lie algebras.
Click on this to see the transparencies of the talks:

These talks are based on the following papers:

For other work on this topic, see: My first talk also refers to this paper:

© 2006 John Baez