John Baez

Joint mathematics/physics talk at Louisiana State University, November 16, 2006
Mathematics colloquium at Stanford University, December 7, 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 Lie groups by Lie 2-groups, bundles by 2-bundles, and so on. Some interesting examples of these concepts show up in the mathematics of topological quantum field theory, string theory and 11-dimensional supergravity.
Click on this to see the transparencies of the talk: This talk is based on the following papers: For more on interpreting Chern-Simons theory as a higher gauge theory, see: For more on interpreting M-theory and 11-dimensional supergravity as higher gauge theories, see: and my expository treatment near the end of week237 of This Week's Finds.

For other work on higher gauge theory, see:

© 2006 John Baez