SUPERGRAVITY AND MATTER - LINEAR MULTIPLET COUPLINGS AND KAHLER ANOMALY CANCELLATION

We present in detail the properties of a linear multiplet in interaction with supergravity and matter, with a special emphasis on the coupling of Chern-Simons forms, relevant for the problem of the chiral and conformal anomalies in relation with Kahler transformations and the corresponding anomaly cancellations. The linear supermultiplet describes an antisymmetric tensor gauge field together with a dilaton and a Majorana spinor. In particular, these fields are found among the massless modes of superstring theories. We review the general properties of this supermultiplet in the Kahler superspace formalism and construct the complete supersymmetric action. This includes the classically Kahler invariant component field action for all the kinetic terms as well as a Green-Schwarz type action which exhibits a non-holomorphic gauge coupling function.