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Equivariant Rozansky-Witten classes and TFTs. (English) Zbl 1261.81099

Summary: We first construct the Rozansky-Witten model coupled to BF theory and Chern-Simons theory using the Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) method. Then we apply the machinery developed in some earlier papers about AKSZ theories and characteristic classes to these concrete models: the BF-Rozansky-Witten model and the Chern-Simons-Rozansky-Witten model. In the former case, we obtain characteristic classes on the target hyperKähler manifold equipped with a group action as a generalization of the original Rozansky-Witten classes. We also give the prescription for similar classes associated with a holomorphic symplectic manifold and demonstrate the invariance of such classes explicitly.

MSC:

81T45 Topological field theories in quantum mechanics
54D45 Local compactness, \(\sigma\)-compactness
58J28 Eta-invariants, Chern-Simons invariants
57R20 Characteristic classes and numbers in differential topology
58A50 Supermanifolds and graded manifolds
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