Building on the superspace formulation for four-dimensional N=2 matter-coupled supergravity developed in arXiv:0805.4683, we elaborate upon a general setting for field theory in N=2 conformally flat superspaces, and concentrate specifically on the case of anti-de Sitter (AdS) superspace. We demonstrate, in particular, that associated with the N=2 AdS supergeometry is a unique vector multiplet such that the corresponding covariantly chiral field strength W_0 is constant, W_0=1. This multiplet proves to be intrinsic in the sense that it encodes all the information about the N=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 N=2 supergravity, also naturally occurs for arbitrary conformally flat superspaces. An explicit superspace reduction N=2 to N=1 is performed for the action principle in general conformally flat N=2 backgrounds, and examples of such reduction are given.
研究了玻色子空间的AdS_mxS ^n几何陪集超空间的超共形结构.特别地，我们证明了陪集流形AdS_2 x S^2，AdS_3 x S^3和AdS_5 x S^5的常规超空间扩张不是超共形平坦的，尽管它们的玻色子子流形是共形平坦的，这些超空间扩张是作为相应的D= 4，6，10超引力的解而产生的，并结合AdS/CFT对应得到了广泛的研究.我们给出了一个组理论推理这一事实。我们发现，在AdS_2 × S^2和AdS_3 × S^3情形下，存在不同的基于超群OSp（4^*）的超陪集|2）超共形平坦。我们还证明了在D= 2，3，4，5中存在超共形平坦的“纯”AdS_D超陪集.提出了超共形平坦性的两种检验方法。一种是求解Maurer-Cartan结构方程，另一种是将AdS_m x S^n超空间的等距超群嵌入到（m+n）维Minkowski空间的超共形群中.最后，我们讨论了上述结果在描述超对称动力系统中的一些应用。
