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Recent advances in curved N=2 superspace methods have rendered the componentreduction of superspace actions more feasible than in the past. In this paper,we consider models involving both vector and tensor multiplets coupled tosupergravity and demonstrate explicitly how component actions may beefficiently obtained. In addition, tensor multiplets coupled to conformalsupergravity are considered directly within projective superspace, where theirformulation is most natural. We then demonstrate how the inverse procedure --the lifting of component results to superspace -- can simplify the analysis ofcomplicated multiplets. We address the off-shell N=2 vector-tensor multipletcoupled to conformal supergravity with a central charge and demonstrateexplicitly how its constraints and Lagrangian can be written in a simpler wayusing superfields.

Component reduction in N=2 supergravity: the vector, tensor, and vector-tensor multiplets