Unification of twistors and Ramond vectors: transmutation of superconformal boosts into local supersymmetry

The relation between the scale and conformal symmetries in the presence of supersymmetry is studied and new supersymmetric twistors dual to the supertwistors are constructed. The dual twistor, called the θ-twistor, includes the composite Ramond vector [11] well known from the spinning string/particle dynamics. It is shown that the spin structure introduced by θ-twistor breaks superconformal symmetry but still preserves global supersymmetry and scale symmetry generalizing the Gross-Wess mechanism for bosonic scattering amplitudes. We establish that the half of the broken D = 4, N = 1 (super)conformal boosts is restored in the form of local supersymmetry.