Generalized supersymmetry and sigma models

In this paper, we discuss the generalizations of exact supersymmetries present in the supersymmetrized sigma models. These generalizations are made by making the supersymmetric transformation parameter field-dependent. Remarkably, the supersymmetric effective actions emerge naturally through the Jacobian associated with the generalized supersymmetry transformations. We explicitly demonstrate these for two different supersymmetric sigma models, namely, one-dimensional sigma model and topological sigma model for hyperinstantons on quaternionic manifold.