First-order higher curvature supergravities and effective theories of strings

A first-order formulation of higher curvature supergravities in the group manifold approach leads to non-trivial torsion equations. In second-order form the resulting Lagrangians exhibit a non-polynomial structure in the curvatures of the basic fields, as well as in the supersymmetry variations. The relevance of these results for the search of superstring compactification is pointed out. The Chapline-Manton Lagrangian is recovered in first-order form and the supersymmetric completion of Chern-Simons terms in five and ten dimensions is considered.