Infinite Dimensional Chern-Simons Theory

Details Infinite Dimensional Chern-Simons Theory Infinite Dimensional Chern-Simons Theory

2004-11-08

arxiv.org/abs/math/0411161v1

Mathematics

Differential Geometry

Scientific paper

We extend finite dimensional Chern-Simons theory to certain infinite dimensional principal bundles with connections, in particular to the frame bundle $FLM\to LM$ over the loop space of a Riemannian manifold $M$. Chern-Simons forms are defined roughly as in finite dimensions with the invariant polynomials replaced by appropriate Wodzicki residues. This produces odd dimensional $\R/\Z$-valued cohomology classes on $LM$ if $M$ is parallelizable. We compute an example of a metric on the loop space of $S^3\times S^1$ for which the three dimensional Chern-Simons class is nontrivial.

Affiliated with

Also associated with

No associations

Rating

Infinite Dimensional Chern-Simons Theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Infinite Dimensional Chern-Simons Theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Infinite Dimensional Chern-Simons Theory will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-109490