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

Govil, Karan; Gunaydin, Murat

doi:10.1007/JHEP03(2015)026

Title: Deformed twistors and higher spin conformal (super-)algebras in four dimensions

Journal Article · Thu Mar 05 00:00:00 EST 2015 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP03(2015)026· OSTI ID:1440969

Govil, Karan ^[1]; Gunaydin, Murat ^[2]

Pennsylvania State Univ., University Park, PA (United States). Inst. for Gravitation and the Cosmos, Dept of Physics
Pennsylvania State Univ., University Park, PA (United States). Inst. for Gravitation and the Cosmos, Dept of Physics; European Organization for Nuclear Research (CERN), Geneva (Switzerland). Theory Division, Physics Dept.

Massless conformal scalar field in d = 4 corresponds to the minimal unitary representation (minrep) of the conformal group SU(2, 2) which admits a one-parameter family of deformations that describe massless fields of arbitrary helicity. The minrep and its deformations were obtained by quantization of the nonlinear 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 irreducible representations can be written as bilinears of deformed twistorial oscillators which transform nonlinearly under the Lorentz group and apply them to define and study higher spin algebras and superalgebras in AdS ₅. The higher spin (HS) algebra of Fradkin-Vasiliev type in AdS₅ is simply the enveloping algebra of SU(2, 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 AdS₅. Furthermore, the enveloping algebras of the deformations of the minrep define a one parameter family of HS algebras in AdS₅ for which certain 4d covariant deformations of the Joseph ideal vanish identically. These results extend to superconformal algebras SU(2, 2|N) and we find a one parameter family of HS superalgebras as enveloping algebras of the minimal unitary supermultiplet and its deformations. Our results suggest the existence of a family of (supersymmetric) HS theories in AdS 5 which are dual to free (super)conformal field theories (CFTs) or to interacting but integrable (supersymmetric) CFTs in 4d. We also discuss the corresponding picture in HS algebras in AdS 4 where the corresponding 3d conformal group Sp(4,R) admits only two massless representations (minreps), namely the scalar and spinor singletons.

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Research Organization:: Pennsylvania State Univ., University Park, PA (United States)

Sponsoring Organization:: USDOE Office of Science (SC); National Science Foundation (NSF)

Grant/Contract Number:: SC0010534; PHY-1213183; PHY-08-55356

OSTI ID:: 1440969

Journal Information:: Journal of High Energy Physics (Online), Vol. 2015, Issue 3; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 18 works

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