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.

54 pages; V2: typos corrected, references, comments and conclusion added; V3: minor typos corrected