Morse Theory in Field Theory

Abstract:
In resent years it becomes apparent that topological field theories (TFTs) are likely the best candidates for truly fundamental physical theory. Supersymmetry, for instance, can be motivated and expressed in terms of TFTs. Here I build simple example of TFT using Morse theory and Massey product. Action (invariant under
supersymmertic transformations) is constructed and relations for correlators in this theory are obtained. During making this theory theorem about connection between Euler characteristic of a manifold and sum of indexes of critical points is proved for arbitrary dimension of the target space.