AdS superprojectors

TL;DR

This paper develops superprojectors in AdS supersymmetry that isolate conserved supercurrents, explores their relation to massless and partially massless multiplets, and constructs models for massive supermultiplets.

Contribution

It introduces superspin projection operators in AdS supersymmetry, analyzes their poles for massless states, and systematically realizes unitary and partially massless supermultiplets.

Findings

Superprojectors map tensor superfields to conserved supercurrents.

Poles of superprojectors correspond to (partially) massless multiplets.

Gauge-invariant actions factorize into minimal second-order operators.

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.