I am reading some aspects of Mirror Symmetry and in mirror symmetry the $N=2$ SCFT on a Calabi Yau Manifold can be divided into two sectors each of which is a topological sigma model, A-Model and B-Model. After some research through some literature about the topological models, it seems that the topological models are constructed only on supersymmetric theory.

Are there any non -Supersymmetric topological sigma models?

Are there some topological models where the target space is not a Calabi-Yau manifold (or in general a Kahler manifold)?

marka sentence as aquestionfor people skimming. Second, I have modified the title to encapsulate the thrust of the question, and set it in the form of a question. – Theo Johnson-Freyd Nov 1 '10 at 18:07