Superform formulations for off-shell supermultiplets with gauged central charge in N=2 supergravity

In N = 2 conformal supergravity in four spacetime dimensions, there exist o -shell supermultiplets with intrinsic central charge, including the Fayet-Sohnius hypermultiplet, the vector-tensor (VT) multiplet and the linear multiplet. Here we construct superform formulations for such multiplets and their variants. To begin with, we review superspace formulations for four-dimensional N = 2 conformal supergravity. We consider models involving both vector and tensor multiplets coupled to supergravity and demonstrate explicitly how component actions may be e ciently obtained with the use of superspace techniques. We introduce the VT multiplets in N = 2 Poincare and AdS supersymmetry. In particular, we discuss the linear and nonlinear VT multiplets. A general setting for N = 2 AdS supersymmetric theories with central charge is presented. A supersymmetric action principle is given in N = 2 AdS superspace and then reformulated in terms of N = 1 super- elds. A proof is presented of the nonexistence of a linear VT multiplet in N = 2 AdS supersymmetry. For the nonlinear VT multiplet, we derive consistent super eld constraints in the presence of any number of N = 2 Yang-Mills vector multiplets, give the supersymmetric action and elaborate on the N = 1 super eld and component descriptions of the theory. In supergravity, we present superform formulations for two versions of VT multiplets and their Chern-Simons couplings. One of them is the standard VT multiplet with the central charge gauged by a vector multiplet. The other is the variant VT multiplet with the property that its own one-form gauges the central charge.