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Odd Chern-Simons Theory, Lie Algebra Cohomology and Characteristic Classes
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
2010 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 300, no 3, 789-833 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2010. Vol. 300, no 3, 789-833 p.
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:uu:diva-145229DOI: 10.1007/s00220-010-1102-zISI: 000285787400009OAI: oai:DiVA.org:uu-145229DiVA: diva2:395673
Available from: 2011-02-07 Created: 2011-02-07 Last updated: 2017-12-11Bibliographically approved

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Qiu, JianZabzine, Maxim

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