SUPERGRAVITY AND MATTER - LINEAR MULTIPLET COUPLINGS AND KAHLER ANOMALY CANCELLATION

We present in detail the properties of a linear multiplet in interacti on with supergravity and matter, with a special emphasis on the coupli ng of Chern-Simons forms, relevant for the problem of the chiral and c onformal anomalies in relation with Kahler transformations and the cor responding anomaly cancellations. The linear supermultiplet describes an antisymmetric tensor gauge field together with a dilaton and a Majo rana spinor. In particular, these fields are found among the massless modes of superstring theories. We review the general properties of thi s supermultiplet in the Kahler superspace formalism and construct the complete supersymmetric action. This includes the classically Kahler i nvariant component field action for all the kinetic terms as well as a Green-Schwarz type action which exhibits a non-holomorphic gauge coup ling function.