Embedding formalism for AdS superspaces in five dimensions

The standard geometric description of d-dimensional anti-de Sitter (AdS) space is a quadric in ℝd−1,2 defined by (X0)2 − (X1)2 − ⋯ − (Xd−1)2 + (Xd)2 = ℓ2 = const. In this paper we provide a supersymmetric generalisation of this embedding construction in the d = 5 case. Specifically, a bi-supertwistor realisation is given for the 𝑁-extended AdS superspace AdS5∣8𝑁, with 𝑁 ≥ 1. The proposed formalism offers a simple construction of AdS super-invariants. As an example, we present a new model for a massive superparticle in AdS5∣8𝑁 which is manifestly invariant under the AdS isometry supergroup SU(2, 2|𝑁) and involves two independent two-derivative terms.