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

Govil, Karan; Günaydın, Murat

doi:10.48550/arxiv.1312.2907

Cited by 8 publications

(15 citation statements)

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“…Quasiconformal realizations of the singletons of Sp(2n, R) coincide with their realizations as bilinears of oscillators transforming covariantly under the maximal compact subgroup U (n) [21]. The Joseph ideal vanishes identically for the singletons [13]. As a consequence the enveloping algebra of the AdS 4 group SO(3, 2) ≡ Sp(4, R) realized as bilinears of covariant twistorial oscillators leads directly to the Fradkin-Vasiliev higher spin algebra as was first pointed out in [15].…”

Section: Introductionmentioning

confidence: 98%

“…The minimal unitary realizations of SU (2, 2|N ) and of OSp(8 * |2N ) and their deformations obtained via quasiconformal methods [1][2][3] were reformulated as bilinears of deformed twistorial oscillators which transform nonlinearly under the Lorentz group in [13,14]. Furthermore it was shown that the enveloping algebras of the minimal unitary realizations of SU (2, 2) and SO * (8) thus obtained lead directly to the higher spin algebras in AdS 5 and AdS 7 .…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, for the doubletonic realizations of the minreps of SO(4, 2) and SO(6, 2) as bilinears of twistorial oscillators transforming covariantly under the respective Lorentz groups, the Joseph ideal does not vanish identically as operators. However it was shown in [13,14] that for the minreps of SO(4, 2) and SO(6, 2) obtained by quasiconformal methods, the Joseph ideals vanish identically as operators. Therefore their enveloping algebras provide unitary realizations of the bosonic higher spin algebras in AdS 5 and AdS 7 , respectively.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore their enveloping algebras provide unitary realizations of the bosonic higher spin algebras in AdS 5 and AdS 7 , respectively. The enveloping algebras of the deformed minreps of SU (2, 2) and of SO * (8) and their supersymmetric extensions lead to infinite families of higher spin algebras and superalgebras in AdS 5 and AdS 7 , respectively [13,14].…”

Section: Introductionmentioning

confidence: 99%

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Massless conformal fields, AdS(+1)/CFT higher spin algebras and their deformations

Fernando

Günaydın

2016

Nuclear Physics B

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We extend our earlier work on the minimal unitary representation of SO(d, 2) and its deformations for d = 4, 5 and 6 to arbitrary dimensions d. We show that there is a one-to-one correspondence between the minrep of SO(d, 2) and its deformations and massless conformal fields in Minkowskian spacetimes in d dimensions. The minrep describes a massless conformal scalar field, and its deformations describe massless conformal fields of higher spin. The generators of Joseph ideal vanish identically as operators for the quasiconformal realization of the minrep, and its enveloping algebra yields directly the standard bosonic AdS (d+1) /CF T d higher spin algebra. For deformed minreps the generators of certain deformations of Joseph ideal vanish as operators and their enveloping algebras lead to deformations of the standard bosonic higher spin algebra. In odd dimensions there is a unique deformation of the higher spin algebra corresponding to the spinor singleton. In even dimensions one finds infinitely many deformations of the higher spin algebra labelled by the eigenvalues of Casimir operator of the little group SO(d − 2) for massless representations.

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Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Massless conformal fields, AdS(+1)/CFT higher spin algebras and their deformations

Fernando

Günaydın

2016

Nuclear Physics B

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“…The spectrum of constituent gauge fields fits into the representation of underlying higher-spin superalgebra and decomposes into an infinite sum of massless representations of SU(2, 2|N) with spins ranging from zero to infinity (see [21] and references therein). More recently it was shown that these superalgebras admit the realization in terms of deformed twistors as enveloping algebras of SU(2, 2|N) [22].…”

Section: Introductionmentioning

confidence: 99%

Ambitwistors, oscillators and massless fields on AdS5

Uvarov

2016

Physics Letters B

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Positive energy unitary irreducible representations of SU (2, 2) can be constructed with the aid of bosonic oscillators in (anti)fundamental representation of SU (2) L × SU (2) R that are closely related to Penrose twistors. Starting with the correspondence between the doubleton representations, homogeneous functions on projective twistor space and on-shell generalized Weyl curvature SL(2, C) spinors and their low-spin counterparts, we study in the similar way the correspondence between the massless representations, homogeneous functions on ambitwistor space and, via the Penrose transform, with the gauge fields on Minkowski boundary of AdS 5 . The possibilities of reconstructing massless fields on AdS 5 and some applications are also discussed.

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Notes on higher-spin algebras: minimal representations and structure constants

Joung

Mkrtchyan

2014

J. High Energ. Phys.

148

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The higher-spin (HS) algebras relevant to Vasiliev's equations in various dimensions can be interpreted as the symmetries of the minimal representation of the isometry algebra. After discussing this connection briefly, we generalize this concept to any classical Lie algebra and consider the corresponding HS algebras. For sp 2N and so N , the minimal representations are unique so we get unique HS algebras. For sl N , the minimal representation has one-parameter family, so does the corresponding HS algebra. The so N HS algebra is what underlies the Vasiliev theory while the sl 2 one coincides with the 3D HS algebra hs [λ]. Finally, we derive the explicit expression of the structure constant of these algebras -more precisely, their bilinear and trilinear forms. Several consistency checks are carried out for our results.

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

Cited by 8 publications

References 0 publications

Massless conformal fields, AdS(+1)/CFT higher spin algebras and their deformations

Massless conformal fields, AdS(+1)/CFT higher spin algebras and their deformations

Ambitwistors, oscillators and massless fields on AdS5

Notes on higher-spin algebras: minimal representations and structure constants

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