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Journal Article

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


Gunaydin,  Murat
AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Govil, K., & Gunaydin, M. (2015). Deformed Twistors and Higher Spin Conformal (Super-)Algebras in Four Dimensions. Journal of high energy physics: JHEP, 2015(03): 26. doi:10.1007/JHEP03(2015)026.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0015-7E3F-A
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 AdS_5 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 AdS_5. Furthermore, the enveloping algebras of
the deformations of the minrep define a one parameter family of HS algebras in
AdS_5 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 AdS_4
where the 3d conformal group Sp(4,R) admits only two massless representations
(minreps), namely the scalar and spinor singletons.