CHERN-SIMONS COUPLINGS AND INEQUIVALENT VECTOR-TENSOR MULTIPLETS

The off-shell vector-tensor multiplet is considered in an arbitrary background of N = 2 vector supermultiplets. We establish the existence of two inequivalent versions, characterized by different Chern-Simons couplings. In one version the vector field of the vector-tensor multiplet is contained quadratically in the Chem-Simons term, which implies non-linear terms in the supersymmetry transformations and equations of motion. In the second version, which requires a background of at least two abelian vector supermultiplets, the supersymmetry transformations remain at most linear in the vector-tensor components. This version is of the type known to arise from reduction of tensor supermultiplets in six dimensions. Our work applies to any number of vector-tensor multiplets.