Sergei M. Kuzenko, Ulf Lindstrom, Gabriele Tartaglino-Mazzucchelli
We introduce N-extended (p,q) AdS superspaces in three space-time dimensions, with p+q=N and p$\geq$q, and analyse their geometry. We show that all (p,q) AdS superspaces with $X^{IJKL}=0$ are conformally flat. Nonlinear sigma-models with (p,q) AdS supersymmetry exist for p+q$\leq$4. Here we concentrate on studying off-shell N=3 supersymmetric sigma-models in AdS_3. For each of the cases (3,0) and (2,1), we give three different realisations of the supersymmetric action. We show that (3,0) AdS supersymmetry requires the sigma-model to be superconformal, and hence the corresponding target space is a hyperkahler cone. In the case of (2,1) AdS supersymmetry, the sigma-model target space must be a non-compact hyperkahler manifold endowed with a Killing vector field which generates an SO(2) group of rotations of the two-sphere of complex structures.
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http://arxiv.org/abs/1205.4622
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