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2D and 3D topological field theories for generalized complex geometry. (English) Zbl 1206.81118
Summary: Using the Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) prescription we construct 2D and 3D topological field theories associated to generalized complex manifolds. These models can be thought of as 2D and 3D generalizations of A- and B-models. Within the BV framework we show that the 3D model on a two-manifold cross an interval can be reduced to the 2D model.

MSC:
81T45 Topological field theories in quantum mechanics
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