Embedding formalism for AdS superspaces in five dimensions

The standard geometric description of \(d\)-dimensional anti-de Sitter (AdS) space is a quadric in \({\mathbb R}^{d-1,2}\) defined by \((X^0)^2 - (X^1)^2 - \dots - (X^{d-1})^2 + (X^d)^2 = \ell^2 = \text{const}\). 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 \({\cal N}\)-extended AdS superspace \(\text{AdS}^{5|8\cal N}\), with \({\cal N}\geq 1\). The proposed formalism offers a simple construction of AdS super-invariants. As an example, we present a model for a massive superparticle in \(\text{AdS}^{5|8\cal N}\) which is manifestly invariant under the AdS isometry supergroup \(\mathsf{SU}(2,2|{\cal N})\).