A review of the group manifold approach and its application to conformal supergravity

An introductory review of the group manifold method is followed by the reconstruction of N = 1 conformal supergravity. New results are: a derivation of the χ-space constraints as field equations and a duality relation between the dilaton and axion curvatures that results in a purely geometric second-order action without Maxwell term. New ideas are: the group manifold used contains no coordinates corresponding to conformal boosts and S-supersymmetry, and rheonomic symmetry is obtained by breaking the O(2) symmetry between Q and S supersymmetry via Lagrange multiplier one-forms.