Abstract. 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 λ α in addition to conventional odd variables θ α . This idea is similar to the Pure Spinor construction. This paper is a short review of papers [11,12]. Original results discussed below were obtained in collaboration with V. Alexandrov, A. Gorodentsev, A. Losev and V. Lysov.
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