Composite Supersymmetries in low - dimensional systems

Starting from a N = 1 scalar supermultiplet in 2+1 dimensions, we demonstrate explicitly the appearance of induced N = 1 vector and scalar supermultiplets of composite operators made out of the fundamental supersymmetric constituents. We discuss an extension to a N = 2 super-algebra with central extension, due to the existence of topological currents in 2+1 dimensions. As a specific model we consider a supersymmetric CP 1 σ-model as the constituent theory, and discuss the relevance of these results for an effective description of the infrared dynamics of planar high-temperature superconducting condensed matter models with quasiparticle excitations near nodal points of their Fermi surface.