General relationship between linear and nonlinear realisations of supersymmetry

Abstract

The close correspondence between the superfield approach to the supersymmetry and the Volkov-Akulov nonlinear realisation is established. The authors show that any superfield, by certain field-dependent changes of variables xmu , theta alpha , can be transformed to the form in which it is represented by nonlinearly transforming components. Conversely, there always exist functions of the nonlinear realisation objects which transform according to the linear supertransformation law. The authors derive general theorems and explicit formulae which describe the transition from the linear realisation to the nonlinear one and vice-versa.