John Baez

22nd British Topology Meeting

September 10, 2007

Higher Gauge Theory and the String Group

Higher gauge theory is a generalization of gauge theory that describes the parallel transport not just of particles, but also strings or higher-dimensional branes. To handle strings, we categorify familiar notions from gauge theory and consider "principal 2-bundles" with a given "structure 2-group". These are a slight generalization of nonabelian gerbes. We focus on examples related to the 2-group Stringk(G) associated to any compact simple Lie group G. We describe how this 2-group is built using the level-k central extension of the loop group of G, and how it is related to the "string group". Finally, we discuss 2-bundles with Stringk(G) as structure 2-group, and pose the problem of computing characteristic classes for such 2-bundles in terms of connections.

Click on this to see the transparencies of the talk:

This talk is based on joint work with Toby Bartels, Alissa Crans, Danny Stevenson and Urs Schreiber: The last reference above begins to tackle the "nice problem" mentioned on the last page of my talk.

For more on the string group, see this:

For closely related work on higher gauge theory, see:

© 2007 John Baez