Abstract
A self-contained superfield approach to global supersymmetry in anti-de Sitter space (OSp(1,4)) is developed. General transformation laws for OSp(1,4) superfields are established, and all basic elements of the OSp(1,4)-covariant formalism, such as covariant superfield derivatives, invariant integration measures over the superspace OSp(1,4)/O(1,3) in both the real and shifted bases, relations between different parametrisations of superspace, etc., are given explicitly. The reducibility questions are analysed, focusing in particular on the structure of chiral representations of OSp(1,4). The simplest linear OSp(1,4)-invariant models are constructed: the OSp(1,4) analogue of the Wess-Zumino model and OSp(1,4) extension of the Yang-Mills theory. The first model, together with the spontaneous breaking of OSp(1,4), exhibits an effect of the spontaneous violation of P and CP parties with the strength related to the anti-de Sitter radius. The relation of the proposed approach to supergravity is discussed.