LINEAR SUPERMULTIPLETS AND NONHOLOMORPHIC GAUGE COUPLING FUNCTIONS

We construct the general couplings of linear multiplets, including Chem-Simons forms, to chiral matter as well as to the standard supergravity-matter system. Insisting on a canonically normalized Einstein term we discuss in particular the appearance of non-holomorphic gauge couplings and perform duality transformations in full generality. We present the implications of these structures for the effective description of sigma model anomalies, with and without coupling to supergravity, following recent proposals of Derendinger, Ferrara, Kounnas and Zwirner and of Cardoso and Ovrut.