Odd Chern-Simons Theory, Lie Algebra Cohomology and Characteristic Classes

Details Odd Chern-Simons Theory, Lie Algebra Cohomology and Characteristic Classes Odd Chern-Simons Theory, Lie Algebra Cohomology and Characteristic Classes

2009-12-07

arxiv.org/abs/0912.1243v2

Commun.Math.Phys.300:789-833,2010

Physics

High Energy Physics

High Energy Physics - Theory

52 pages

Scientific paper

10.1007/s00220-010-1102-z

We investigate the generic 3D topological field theory within AKSZ-BV framework. We use the Batalin-Vilkovisky (BV) formalism to construct explicitly cocycles of the Lie algebra of formal Hamiltonian vector fields and we argue that the perturbative partition function gives rise to secondary characteristic classes. We investigate a toy model which is an odd analogue of Chern-Simons theory, and we give some explicit computation of two point functions and show that its perturbation theory is identical to the Chern-Simons theory. We give concrete example of the homomorphism taking Lie algebra cocycles to Q-characteristic classes, and we reinterpreted the Rozansky-Witten model in this light.

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