There are special such superconformal multiplet, which have no analog as super Poincare multiplet, called supesingletons, first observe by (Dirac 63)

References

P. A. M. Dirac, A remarkable representation of the 3+2 de Sitter group, J. Math. Phys. 4 (1963) 901.

C. Fronsdal, Dirac supermultiplet, Phys. Rev. D26 (1982) 1988.

M. Flato and C. Fronsdal, Quantum field theory of singletons. The rac, J. Math. Phys. 22 (1981) 1100

Murat Günaydin, Singleton and doubleton supermultiplets of space-time supergroups and infinite spin superalgebras, in Mike Duff, Christopher Pope and Ergin Sezgin (eds.) Proceedings of the 1989 Trieste Conference “Supermembranes and Physics in 2 + 1 Dimensions”, World Scientific 1990

Mike Duff, Anti-de Sitter space, branes, singletons, superconformal field theories and all that, Int.J.Mod.Phys.A14:815-844,1999 (arXiv:hep-th/9808100)

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