Rigid 4D N=2 supersymmetric backgrounds and actions

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We classify all N=2 rigid supersymmetric backgrounds in four dimensions with both Lorentzian and Euclidean signature that preserve eight real supercharges, up to discrete identifications. Among the backgrounds we find specific warpings of S³ x R and AdS₃ x R, AdS₂ x S² and H² x S² with generic radii, and some more exotic geometries. We provide the generic two-derivative rigid vector and hypermultiplet actions and analyze the conditions imposed on the special Kahler and hyperkahler target spaces.