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)overset{cdot }{alpha }(n)}:= {mathfrak{V}}_{left(alpha 1dots alpha mright)left({overset{cdot }{alpha}}_1dots {overset{cdot }{alpha}}_nright)} on AdS superspace, with m and n non-negative integers, the corresponding superprojector turns {mathfrak{V}}_{alpha (m)overset{cdot }{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 AdS4 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 AdS4. We also prove that the gauge-invariant actions for superconformal higher-spin multiplets factorise into products of minimal second-order differential operators.
Highlights
Superprojectors [1,2,3,4,5,6,7] are superspace projection operators which single out irreducible representations of supersymmetry
Of special interest are those superprojectors which single out the highest superspin of tensor superfields Vα(m)α (n)(x, θ, θ) := Vα1...αmα 1...αn (x, θ, θ) = V(α1...αm)(α 1...αn)(x, θ, θ), since they may be viewed as supersymmetric extensions of the Behrends-Fronsdal spin projection operators [13, 14]
Not much is known about the structure of superprojectors corresponding to the AdS4 supersymmetry OSp(1|4)
Summary
Superprojectors [1,2,3,4,5,6,7] are superspace projection operators which single out irreducible representations of supersymmetry. [15] described the projectors to the spaces of superfields which are constrained by (1.2), (1.3) and (1.4), see eq (3.10) below These are not supersymmetric extensions of the Behrends-Fronsdal spin projection operators [13, 14], since all independent component fields of the resulting superfield are unconstrained. Irreducible unitary representations of the N = 1 AdS4 superalgebra osp(1|4), which we will call supermultiplets, are conveniently described by decomposing them into irreducible representations of so(3, 2) in analogy with the case of the super Poincaré algebra in flat space. The corresponding representations are called massless and are of the form This implies that a massless supermultiplet in AdS4 consists of two physical component fields. The Wess-Zumino supermultiplets (2.2) correspond to the superspin-0 representations
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