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

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Abstract

We investigate the generic 3D topological field theory within the 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 a concrete example of the homomorphism taking Lie algebra cocycles to Q-characteristic classes, and we reinterpret the Rozansky-Witten model in this light.

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Authors and Affiliations

  1. Department of Physics and Astronomy, Uppsala University, Box 516, SE-75120, Uppsala, Sweden

    Jian Qiu & Maxim Zabzine

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  1. Jian Qiu
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  2. Maxim Zabzine
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Correspondence to Jian Qiu.

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Communicated by A. Kapustin

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Qiu, J., Zabzine, M. Odd Chern-Simons Theory, Lie Algebra Cohomology and Characteristic Classes. Commun. Math. Phys. 300, 789–833 (2010). https://doi.org/10.1007/s00220-010-1102-z

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  • DOI: https://doi.org/10.1007/s00220-010-1102-z

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