Three Dimensional Topological Field Theory induced from Generalized Complex Structure

TL;DR

This paper constructs a three-dimensional topological sigma model based on generalized complex structures, demonstrating invariance under key symmetries and connecting to known models like Zucchini's and WZ-Poisson manifolds.

Contribution

It introduces a novel 3D topological sigma model derived from generalized complex geometry, unifying various models and symmetries in a new framework.

Findings

Model is invariant under diffeomorphisms and b-transformations.

Derives 2D boundary sigma model from the 3D model.

Realizes WZ-Poisson manifold in three dimensions.

Abstract

We construct a three-dimensional topological sigma model which is induced from a generalized complex structure on a target generalized complex manifold. This model is constructed from maps from a three-dimensional manifold $X$ to an arbitrary generalized complex manifold $M$. The theory is invariant under the diffeomorphism on the world volume and the $b$-transformation on the generalized complex structure. Moreover the model is manifestly invariant under the mirror symmetry. We derive from this model the Zucchini's two dimensional topological sigma model with a generalized complex structure as a boundary action on $\partial X$. As a special case, we obtain three dimensional realization of a WZ-Poisson manifold.