Embedding formalism for AdS superspaces in five dimensions

Abstract

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 new model for a massive superparticle in $\text{AdS}^{5|8\cal N}$ which is manifestly invariant under the AdS isometry supergroup $\mathsf{SU}(2,2|{\cal N})$ and involves two independent two-derivative terms.