Embedding formalism for AdS superspaces in five dimensions

Abstract

Abstract The standard geometric description of d-dimensional anti-de Sitter (AdS) space is a quadric in ℝ d−1,2 defined by (X 0)2 − (X 1)2 − ⋯ − (X d−1)2 + (X d )2 = ℓ 2 = 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 $$ \mathcal{N} $$ -extended AdS superspace AdS 5 ∣ 8 N $$ {\textrm{AdS}}^{5\mid 8\mathcal{N}} $$ , with N $$ \mathcal{N} $$ ≥ 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 AdS 5 ∣ 8 N $$ {\textrm{AdS}}^{5\mid 8\mathcal{N}} $$ which is manifestly invariant under the AdS isometry supergroup SU(2, 2| N $$ \mathcal{N} $$ ) and involves two independent two-derivative terms.

Keywords

• Extended Supersymmetry
• Superspaces