Odd Chern-Simons theory and the construction of characteristic classes
OKC/Nordita High-Energy Physics Theory seminar
Monday 30 November 2009
to 14:30 at
Nordita seminar room 132:028
Jian Qiu (Uppsala University)
The perturbation expansion of Chern-Simons theory is rich in its structure. It was shown by Kontsevich that
the perturbation expansion in fact realises a pairing of two dual constructions of graph (co)homology.
One of the above constructions is related to the knot invariants of the 3D manifold on which CS lives, while its dual coonstruction is
related to the Lie algebra cohomology of the gauge group. Inspired by this, we constructed an analogue of
Chern-Simons which is odd (in both senses). This allows us to study and construct cocycles of the Chevalley Eilenberg
complex of the Lie algebra of formal Hamiltonian vector fields. After this one can apply the well known Chern-Weil construction
to obtain characteristic classes of, say, Poisson manifold, Lie algebroids and foliations etc. I will give a physicists' explaination of the
mathematical objects introduced above.