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

TL;DR

This paper constructs 2D and 3D topological field theories based on generalized complex geometry using the AKSZ formalism, extending the concepts of A- and B-models and demonstrating dimensional reduction within the BV framework.

Contribution

It introduces new topological field theories for generalized complex manifolds in 2D and 3D, generalizing existing models and analyzing their reduction properties.

Findings

3D model reduces to 2D model on a two-manifold cross an interval

Models generalize A- and B-models to generalized complex geometry

Framework established within BV formalism

Abstract

Using the 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.