N=2 supersymmetric sigma-models in AdS

We construct the most general N = 2 supersymmetric nonlinear sigma-model in four-dimensional anti-de Sitter (AdS) space in terms of N = 1 chiral superfields. The target space is shown to be a non-compact hyper-Kahler manifold restricted to possess a special Killing vector field. A remarkable property of the sigma-model constructed is that the algebra of OSp(2 vertical bar 4) transformations is closed off the mass shell. (C) 2011 Elsevier B.V. All rights reserved.