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.

This post imported from StackExchange MathOverflow at 2015-04-04 12:48 (UTC), posted by SE-user Moduli