Embedding formalism for AdS superspaces in five dimensions

TL;DR

This paper extends the geometric embedding of AdS space to supersymmetric cases in five dimensions, providing a new formalism that simplifies the construction of super-invariants and introduces a model for a massive superparticle.

Contribution

It introduces a supersymmetric embedding construction for AdS5 superspaces using bi-supertwistors, enabling easier derivation of super-invariants and a new superparticle model.

Findings

Supersymmetric embedding of AdS5 space via bi-supertwistors.

Construction of a superparticle model invariant under AdS supergroup.

Simplification of super-invariant formulation in AdS superspaces.

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.