The descent of off-shell supersymmetry to the mass shell. short review

It is shown that classical actions for some ''physically interesting'' quantum field theories can be obtained as effective actions from the single ''fundamental'' theory of the Chern-Simons form. The physical degrees of freedom are encoded in the space of cohomologies of a certain differential operator. This observation suggests a different perspective on some of the supersymmetric properties of these effective theories. Namely, it is possible to construct a superfield formalism which allows to find off-shell SUSY actions for the on-shell supersymmetric theories, where conventional superfield formalism does not work. This formalism contains even auxiliary variables λα in addition to conventional odd variables θα. This idea is similar to the Pure Spinor construction. (orig.)