2D and 3D topological field theories for generalized complex geometry

Abstract

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.