Abstract
Building on the superspace formulation for four-dimensional = 2 matter-coupled supergravity developed in [1], we elaborate upon a general setting for field theory in = 2 conformally flat superspaces, and concentrate specifically on the case of anti-de Sitter (AdS) superspace. We demonstrate, in particular, that associated with the = 2 AdS supergeometry is a unique vector multiplet such that the corresponding covariantly chiral field strength 0 is constant, 0 = 1. This multiplet proves to be intrinsic in the sense that it encodes all the information about the = 2 AdS supergeometry in a conformally flat frame. Moreover, it emerges as a building block in the construction of various supersymmetric actions. Such a vector multiplet, which can be identified with one of the two compensators of = 2 supergravity, also naturally occurs for arbitrary conformally flat superspaces. An explicit superspace reduction = 2 → = 1 is performed for the action principle in general conformally flat = 2 backgrounds, and examples of such reduction are given.
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