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In this paper we elucidate the rigid limit of N = 2 supergravity coupled to vector and hypermultiplets. In particular we show how the respective scalar field spaces reduce to their global counterparts. In the hypermultiplet sector we focus on the relation between the local and rigid c-map. [ABSTRACT FROM AUTHOR]

We define the worldline harmonic superspace and its analytic subspace as a deformation of the flat harmonic superspace. The harmonic superfield description of the two mutually mirror off-shell supermultiplets is developed and the corresponding invariant actions are presented, as well as the relevant classical and quantum supercharges. Whereas the σ-model actions exist for both types of the multiplet, the invariant Wess–Zumino term can be defined only for one of them, thus demonstrating non-equivalence of these multiplets in the case as opposed to the flat supersymmetry. A superconformal subclass of general actions invariant under the trigonometric-type realizations of the supergroup is singled out. The superconformal Wess–Zumino actions are shown to possess an infinite-dimensional supersymmetry forming the centerless super Virasoro algebra. We solve a few simple instructive examples of the supersymmetric quantum mechanics of the multiplets and reveal the representation contents of the corresponding sets of the quantum states. [ABSTRACT FROM AUTHOR]