The structure of N=2 supersymmetric nonlinear sigma models in AdS4

We present a detailed study of the most general N = 2 supersymmetric sigma models in four-dimensional anti-de Sitter space (AdS(4)) formulated in terms of N = 1 chiral superfields. The target space is demonstrated to be a non-compact hyperkahler manifold restricted to possess a special Killing vector field which generates an SO(2) group of rotations on the two-sphere of complex structures and necessarily leaves one of them invariant. All hyperkahler cones, that is the target spaces of N = 2 superconformal sigma models, prove to possess such a vector field that belongs to the Lie algebra of an isometry group SU(2) acting by rotations on the complex structures. A unique property of the N = 2 sigma models constructed is that the algebra of OSp(2|4) transformations closes off the mass shell. We uncover the underlying N = 2 superfield formulation for the N = 2 sigma models constructed and compute the associated N = 2 supercurrent. We give a special analysis of the most general systems of self-interacting N = 2 tensor multiplets in AdS(4) and their dual sigma models realized in terms of N = 1 chiral multiplets. We also briefly discuss the relationship between our results on N = 2 supersymmetric sigma models formulated in the N = 1 AdS superspace and the off-shell sigma models constructed in the N = 2 AdS superspace in arXiv: 0807.3368.