Embedding formalism for N -extended AdS superspace in four dimensions

The supertwistor and bi-supertwistor formulations for N -extended anti-de Sitter (AdS) superspace in four dimensions, AdS^4∣4N , were derived two years ago in [1]. In the present paper, we introduce a novel realisation of the N -extended AdS supergroup OSp(N |4; ℝ) and apply it to develop a coset construction for AdS^4∣4N and the corresponding differential geometry. This realisation naturally leads to an atlas on AdS^4∣4N (that is a generalisation of the stereographic projection for a sphere) that consists of two charts with chiral transition functions for N > 0. A manifestly OSp(N |4; ℝ) invariant model for a superparticle in AdS^4∣4N is proposed. Additionally, by employing a conformal superspace approach, we describe the most general conformally flat N -extended supergeometry. This construction is then specialised to the case of AdS^4∣4N .