### Higher Gauge Theory

#### Posted by John Baez

On Thursday I’m flying to Baton Rouge to give a talk on higher gauge theory and check out the nearby gravitational wave detector. You can see my slides here:

- John Baez, Higher gauge theory, Mathematics and Physics & Astronomy Departments, Louisiana State University, November 14, 2006.

If you’re an expert on this business, perhaps the only thing you may not have seen yet is a discussion of how $B F$ theory in 4 dimensions is a higher gauge theory.

If you spot typos or other mistakes I would love to hear about them - especially before Thursday morning!

**Abstract:** 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 forthis, 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.

I was invited to give this talk by Jorge Pullin, a long-time colleague of mine who works on loop quantum gravity. I’ll talk with him about that, and meet other mathematicians and physicists, including some working on quantum computation.

Also, on Saturday, I hope to visit the Laser Interferometer Gravitational-Wave Observatory in Livingston Louisiana! This thing is big:

It consists of two tubes, each about 2.5 kilometers long. The goal is to bounce lasers back and forth along these tubes to measure their length with an accuracy of 10^{-19} meters, to see if gravitational ripples are distorting space. For comparison, the radius of a proton is a whopping 10^{-15} meters. So, there’s a tremendous amount of work involved trying to eliminate all forms of error. Jorge’s wife Gabriela González works on this project, trying to understand and eliminate thermal noise.

I’ll try to take some photos and post them here!

## Re: Higher Gauge Theory

Typo: on p. 11, $t$ should go from $H$ to $G$. And again on p. 13.