Equivariant Rozansky-Witten classes and TFTs

TL;DR

This paper constructs new topological field theories combining Rozansky-Witten models with BF and Chern-Simons theories, deriving characteristic classes on hyperKahler and holomorphic symplectic manifolds, and demonstrating their invariance.

Contribution

It introduces coupled Rozansky-Witten models with BF and Chern-Simons theories using the AKSZ method, extending characteristic classes to new geometric contexts.

Findings

Derived characteristic classes on hyperKahler manifolds with group actions

Extended classes to holomorphic symplectic manifolds

Proved invariance of the new characteristic classes

Abstract

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 hyperKahler 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.