N ov 2 00 4 INFINITE DIMENSIONAL CHERN - SIMONS THEORY
نویسندگان
چکیده
We extend finite dimensional Chern-Simons theory to certain infinite dimensional principal bundles with connections, in particular to the frame bundle F LM −→ 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 × S 1 for which the three dimensional Chern-Simons class is nontrivial.
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