John Baez

Workshop on Geometry and Lie Groups, Hong Kong University, March 25, 2011
Quantum Theory and Gravitation, ETH Zürich, June 16, 2011

Higher Gauge Theory, Division Algebras and Superstrings

Classically, superstrings make sense when spacetime has dimension 3, 4, 6, or 10. It is no coincidence that these numbers are two more than 1, 2, 4, and 8, which are the dimensions of the normed division algebras: the real numbers, complex numbers, quaternions and octonions. We sketch an explanation of this already known fact and its relation to "higher gauge theory". Just as gauge theory describes the parallel transport of supersymmetric particles using Lie supergroups, higher gauge theory describes the parallel transport of superstrings using "Lie 2-supergroups". Recently John Huerta has shown that we can use normed division algebras to construct a Lie 2-supergroup extending the Poincaré supergroup when spacetime has dimension 3, 4, 6 or 10. He also used them to construct a Lie 3-supergroup when spacetime has dimension 4, 5, 7 or 11. The 11-dimensional case is related to 11-dimensional supergravity, and thus presumably to "M-theory".

To see the slides click here.
For a version with more math and less physics, try this.

This talk is based on John Huerta's thesis:

His talks go deeper than mine: Also try our papers:

There are many other relevant papers, such as these:

© 2011 John Baez