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Deformed twistors and higher spin conformal (super-)algebras in six dimensions

By U.S.A. PA 16802 University Park Pennsylvania State University Physics Department Karan GovilInstitute for Gravitation and the Cosmos and U.S.A.) PA 16802 University Park Pennsylvania State University Physics Department Murat Günaydin(Institute for Gravitation and the Cosmos

Abstract

Massless conformal scalar field in six dimensions corresponds to the minimal unitary representation (minrep) of the conformal group SO(6, 2). This minrep admits a family of “deformations” labelled by the spin t of an SU(2) T group, which is the 6 d analog of helicity in four dimensions. These deformations of the minrep of SO(6 , 2) describe massless conformal fields that are symmetric tensors in the spinorial representation of the 6 d Lorentz group. The minrep and its deformations were obtained by quantization of the nonlinear realization of SO(6 , 2) as a quasiconformal group in arXiv:1005.3580 . We give a novel reformulation of the generators of SO(6 , 2) for these representations as bilinears of deformed twistorial oscillators which transform nonlinearly under the Lorentz group SO(5 , 1) and apply them to define higher spin algebras and superalgebras in AdS 7 . The higher spin (HS) algebra of Fradkin-Vasiliev type in AdS 7 is simply the enveloping algebra of SO(6 , 2) quotiented by a two-sided ideal (Joseph ideal) which annihilates the minrep. We show that the Joseph ideal vanishes identically for the quasiconformal realization of the minrep and its enveloping algebra leads directly to the HS algebra in AdS 7 . Furthermore, the enveloping algebras of the deformations of the minrep define a discrete infinite family of HS algebras in AdS 7 for which certain 6 d Lorentz covariant deformations of the Joseph ideal vanish identically. These results extend to superconformal algebras OSp(8 * |2 N ) and we find a discrete infinite family of HS superalgebras as enveloping algebras of the minimal unitary supermultiplet and its deformations. Our results suggest the existence of a discrete family of (supersymmetric) HS theories in AdS 7 which are dual to free (super)conformal field theories (CFTs) or to interacting but integrable (supersymmetric) CFTs in 6 d

Year: 2014
DOI identifier: 10.1007/JHEP07(2014)004
OAI identifier: oai:www.openaccessrepository.it:8917

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