Lagrangian description of the partially massless higher spin N=1 supermultiplets in $Ad{S}_4$ space

Abstract

In the recent paper [1] the classification of non-unitary representations of the three dimensional superconformal group has been constructed. From AdS/CFT they must correspond to N=1 supermultiplets containing partially massless fields in $Ad{S}_4$. Moreover, the simplest example of such supermultiplets which contains a partially massless spin-2 was explicitly constructed. In this paper we extend this result and develop explicit Lagrangian construction of general N=1 supermultiplets containing partially massless fields with arbitrary superspin. We use the frame-like gauge invariant description of partially massless higher spin bosonic and fermionic fields. For the two types of the supermultiplets (with integer and half-integer superspins) each one containing two partially massless bosonic and two partially massless fermionic fields we derive the supertransformations leaving the sum of four their free Lagrangians invariant such that the $Ad{S}_4$ superalgebra is closed on-shell.

arXiv comment17 pages; v2: appendix, references and comments added, typos corrected. arXiv admin note: text overlap with arXiv:1901.09637

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• Looking for partially-massless gravity
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• Hierarchy of Supersymmetric Higher Spin Connections
• AdS superprojectors
• Generalised superconformal higher-spin multiplets
• $\mathcal{N}=2$ Supersymmetric Partially Massless Fields and Non-Unitary Superconformal Representations
• Linearized Coxeter Higher-Spin Theories
• Fermionic Shift Symmetries in (Anti) de Sitter Space
• Superspace First Order Formalism, Trivial Symmetries and Electromagnetic Interactions of Linearized Supergravity
• Cubic interactions for massless and partially massless spin-1 and spin-2 fields
• Partially massless spin 2 and supersymmetry
• On massive higher spin supermultiplets in d=4
• Partially massless spin 5/2 and supersymmetry
• On higher spin cubic interactions in d=3
• Superspace First-order Formalism for Massless Arbitrary Superspin Supermultiplets