### Abstract

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)}/CFT_{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.

Original language | English (US) |
---|---|

Pages (from-to) | 494-526 |

Number of pages | 33 |

Journal | Nuclear Physics B |

Volume | 904 |

DOIs | |

State | Published - Mar 1 2016 |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Cite this

}

_{(d+1)}/CFT

_{d}higher spin algebras and their deformations',

*Nuclear Physics B*, vol. 904, pp. 494-526. https://doi.org/10.1016/j.nuclphysb.2016.01.024

**Massless conformal fields, AdS _{(d+1)}/CFT_{d} higher spin algebras and their deformations.** / Fernando, Sudarshan; Gunaydin, Murat.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Massless conformal fields, AdS(d+1)/CFTd higher spin algebras and their deformations

AU - Fernando, Sudarshan

AU - Gunaydin, Murat

PY - 2016/3/1

Y1 - 2016/3/1

N2 - 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)/CFTd 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.

AB - 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)/CFTd 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.

UR - http://www.scopus.com/inward/record.url?scp=84956601757&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84956601757&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2016.01.024

DO - 10.1016/j.nuclphysb.2016.01.024

M3 - Article

VL - 904

SP - 494

EP - 526

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

ER -