Vector-tensor supermultiplets in AdS and supergravity

In N = 2 Poincare supersymmetry in four space-time dimensions, there exist off-shell supermultiplets with intrinsic central charge, including the important examples of the Fayet-Sohnius hypermultiplet, the linear and the nonlinear vector-tensor (VT) multiplets. One can also define similar supermultiplets in the context of N = 2 anti-de Sitter (AdS) supersymmetry, although the origin of the central charge becomes somewhat obscure. In this paper we develop a general setting for N = 2 AdS supersymmetric theories with central charge. We formulate a supersymmetric action principle in N = 2 AdS superspace and then reformulate it in terms of N = 1 superfields. We prove that N = 2 AdS supersymmetry does not allow existence of a linear VT multiplet. For the nonlinear VT multiplet, we derive consistent superfield constraints in the presence of any number of N = 2 Yang-Mills vector multiplets, give the supersymmetric action and elaborate on the N = 1 superfield and component descriptions of the theory. Our description of the nonlinear VT multiplet in AdS is then lifted to N = 2 supergravity. Moreover, we derive consistent superfield constraints and Lagrangian that describe the linear VT multiplet in N = 2 supergravity in the presence of two vector multiplets, one of which gauges the central charge. These supergravity constructions thus provide the first superspace formulation for the component results derived in arXiv:hep-th/9710212. We also construct higher-derivative couplings of the VT multiplet to any number of N = 2 tensor multiplets.