The structure of $ \mathcal{N} = {2} $ supersymmetric nonlinear sigma models in AdS4

Abstract

We present a detailed study of the most general $ \mathcal{N} = {2} $ supersymmetric sigma models in four-dimensional anti-de Sitter space (AdS4) formulated in terms of $ \mathcal{N} = 1 $ chiral superfields. The target space is demonstrated to be a non-compact hyperkähler 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 hyperkähler cones, that is the target spaces of $ \mathcal{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 $ \mathcal{N} = {2} $ sigmamodelsconstructedisthatthealgebraofOSp(2|4)transformationsclosesoff the mass shell. We uncover the underlying $ \mathcal{N} = {2} $ superfield formulation for the $ \mathcal{N} = {2} $ sigma models constructed and compute the associated $ \mathcal{N} = {2} $ supercurrent. We give a special analysis of the most general systems of self-interacting $ \mathcal{N} = {2} $ tensor multiplets in AdS4 and their dual sigma models realized in terms of $ \mathcal{N} = 1 $ chiral multiplets. We also briefly discuss the relationship between our results on $ \mathcal{N} = {2} $ supersymmetric sigma models formulated in the $ \mathcal{N} = 1 $ AdS superspace and the off-shell sigma models constructed in the $ \mathcal{N} = {2} $ AdS superspace in arXiv:0807.3368 .