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 $(X^0{)}^2-(X^1{)}^2-\cdots -(X^{d-1}{)}^2+(X^d{)}^2={\mathrm{\ell }}^2=\text{const}$. 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 $\mathcal{N}$-extended AdS superspace ${\text{AdS}}^{5\mathrm{\mid }8\mathcal{N}}$, with $\mathcal{N}\ge 1$. The proposed formalism offers a simple construction of AdS super-invariants. As an example, we present a new model for a massive superparticle in ${\text{AdS}}^{5\mathrm{\mid }8\mathcal{N}}$ which is manifestly invariant under the AdS isometry supergroup $\mathsf{S}\mathsf{U}(2,2\mathrm{\mid }\mathcal{N})$ and involves two independent two-derivative terms.