Cohomological field theory

An elementary introduction to some generic features of cohomological theories are given, using the four-dimensional model by Witten as example. The action governing the four-dimensional Witten model and its full BRST (Becchi, Rouet, Stora, Tyutin) symmetry is discussed. The action is interpreted as a pure gauge fixing term of a system with zero starting action. The complete set of topologically invariant operators of the model are enumerated. The descent equations that couple their BRST and de Rham cohomologies will be used to elucidate how they end up giving topological invariants even though they are local integrals of fields. The ghost symmetry of the system is discussed, and the explicit evaluation of typical topological invariants is outlined. 12 refs