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Massless conformal scalar field in d=4 corresponds to the minimal unitaryrepresentation (minrep) of the conformal group SU(2,2) which admits aone-parameter family of deformations that describe massless fields of arbitraryhelicity. The minrep and its deformations were obtained by quantization of thenonlinear realization of SU(2,2) as a quasiconformal group in arXiv:0908.3624.We show that the generators of SU(2,2) for these unitary irreduciblerepresentations can be written as bilinears of deformed twistorial oscillatorswhich transform nonlinearly under the Lorentz group and apply them to defineand study higher spin algebras and superalgebras in AdS_5. The higher spin (HS)algebra of Fradkin-Vasiliev type in AdS_5 is simply the enveloping algebra ofSU(2,2) quotiented by a two-sided ideal (Joseph ideal) which annihilates theminrep. We show that the Joseph ideal vanishes identically for thequasiconformal realization of the minrep and its enveloping algebra leadsdirectly to the HS algebra in AdS_5. Furthermore, the enveloping algebras ofthe deformations of the minrep define a one parameter family of HS algebras inAdS_5 for which certain 4d covariant deformations of the Joseph ideal vanishidentically. These results extend to superconformal algebras SU(2,2|N) and wefind a one parameter family of HS superalgebras as enveloping algebras of theminimal unitary supermultiplet and its deformations. Our results suggest theexistence of a family of (supersymmetric) HS theories in AdS_5 which are dualto free (super)conformal field theories (CFTs) or to interacting but integrable(supersymmetric) CFTs in 4d. We also discuss the corresponding picture in AdS_4where the 3d conformal group Sp(4,R) admits only two massless representations(minreps), namely the scalar and spinor singletons.

Deformed Twistors and Higher Spin Conformal (Super-)Algebras in Four Dimensions