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Building on the superspace formulation for four-dimensional N=2matter-coupled supergravity developed in arXiv:0805.4683, we elaborate upon ageneral setting for field theory in N=2 conformally flat superspaces, andconcentrate specifically on the case of anti-de Sitter (AdS) superspace. Wedemonstrate, in particular, that associated with the N=2 AdS supergeometry is aunique vector multiplet such that the corresponding covariantly chiral fieldstrength W_0 is constant, W_0=1. This multiplet proves to be intrinsic in thesense that it encodes all the information about the N=2 AdS supergeometry in aconformally flat frame. Moreover, it emerges as a building block in theconstruction of various supersymmetric actions. Such a vector multiplet, whichcan be identified with one of the two compensators of N=2 supergravity, alsonaturally occurs for arbitrary conformally flat superspaces. An explicitsuperspace reduction N=2 to N=1 is performed for the action principle ingeneral conformally flat N=2 backgrounds, and examples of such reduction aregiven.

Field theory in 4D N=2 conformally flat superspace