AdS superprojectors

Abstract: Within the framework of ${\mathcal N}=1$ anti-de Sitter (AdS) supersymmetry in four dimensions, we derive superspin projection operators (or superprojectors). For a tensor superfield $\mathfrak{V}{\alpha(m)\dot{\alpha} (n)} := \mathfrak{V}{(\alpha_1...\alpha_m) (\dot \alpha_1...\dot \alpha_n)}$ on AdS superspace, with $m$ and $n$ non-negative integers, the corresponding superprojector turns $\mathfrak{V}_{\alpha(m)\dot \alpha(n)} $ into a multiplet with the properties of a conserved conformal supercurrent. It is demonstrated that the poles of such superprojectors correspond to (partially) massless multiplets, and the associated gauge transformations are derived. We give a systematic discussion of how to realise the unitary and the partially massless representations of the ${\mathcal N}=1$ AdS${}_4$ superalgebra $\mathfrak{osp} (1|4)$ in terms of on-shell superfields. As an example, we present an off-shell model for the massive gravitino multiplet in AdS$_4$. We also prove that the gauge-invariant actions for superconformal higher-spin multiplets factorise into products of minimal second-order differential operators.