I am thinking about some topological field theories, and I am wondering when one can say that the stationary phase approximation (ie. a sum of the first-order variations about each vacuum) is exact.
I am looking perhaps for conditions on how the space of vacua is embedded into the space of all field configurations. I suspect that when the action is a Morse function (and I suppose the space of field configurations is finite dimensional) that the exactness of the stationary phase approximation implies some very strict topological constraints on the configuration space... torsion-free and so on.
Anyone have a good reference or some wisdom?
Also I'd like to dedicate this question to the memory of theoreticalphysics.stackexchange