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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)?
I believe that A-model does not require a Calabi-Yau target space. In fact, A-model is well-defined on any almost complex manifold, which was Witten's original construction (Comm. Math. Phys. Volume 118, Number 3 (1988), 411-449). On the other hand, B-model can only be defined on a Calabi-Yau manifold, which follows from anomaly cancelation.
In general, topological field theories have many different types (not necessarily supersymmetric). As an example, Chern-Simons theory is topological. Try http://en.wikipedia.org/wiki/Topological_quantum_field_theory for some general discussion.
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