N = 1, D = 6 Supergravity: Duality and non Minimal Couplings.

Six-dimensional supergravity theories and their duality properties play a central role in the context of string duality and string compactifications. Lowering dimensions leads usually to an increasing complexity of theories; with this respect six dimensions seem to constitute an appropriate compromise between the physical four and the presumably more fundamental ten or eleven dimensions. In this paper we present a superspace formulation of N = 1,D = 6 supergravity with one tensor-multiplet and an arbitrary number of vectorand hypermultiplets, in which the bosonic abelian superforms of the theory, the dilaton, the abelian gauge fields and the two-form are replaced by their S-duals i.e. four, three and two-superforms respectively, in compatibility with supersymmetry. As usual this replacement interchanges Bianchi identities with equations of motion. This formulation holds in the presence of one tensor multiplet and arbitrary numbers of hypermultiplets and abelian super-Maxwell multiplets if all couplings are minimal. We determine the consistency conditions for non-minimal couplings in N = 1, D = 6 supergravity, for which we present a particularly significant solution, namely the one associated with the Chern-Simons-Lorentz three-form which entails the Green-Schwarz anomaly cancellation mechanism. In the case of non minimal couplings it is found that the gauge fields and the two-form can still be dualized while the dilaton has to remain a zero-form. PACS: 04.65.+e;