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 \( {\mathfrak{V}}_{\alpha (m)\overset{\cdot }{\alpha }(n)}:= {\mathfrak{V}}_{\left(\alpha 1\dots \alpha m\right)\left({\overset{\cdot }{\alpha}}_1\dots {\overset{\cdot }{\alpha}}_n\right)} \) 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.
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Buchbinder, E.I., Hutchings, D., Kuzenko, S.M. et al. AdS superprojectors. J. High Energ. Phys. 2021, 74 (2021). https://doi.org/10.1007/JHEP04(2021)074
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DOI: https://doi.org/10.1007/JHEP04(2021)074