Dimensional reduction in supersymmetric field theories

A class of quantum field theories invariant with respect to the action of an odd vector field Q on a source supermanifold Sigma is considered. We suppose that Q satisfies the conditions of one of the localization theorems (Szabo R 1996 Equivariant localization of path integrals Preprint hep-th/9608068). The Q-invariant sector of a field theory from the above class is then shown to be equivalent to the quantum field theory defined on the zero locus of the vector field Q