Massless conformal fields, AdS _{(d+1)}/CFT _{d} higher spin algebras and their deformations
Here, we extend our earlier work on the minimal unitary representation of SO(d, 2)and its deformations for d=4, 5and 6to arbitrary dimensions d. We show that there is a onetoone correspondence between the minrep of SO(d, 2)and its deformations and massless conformal fields in Minkowskian spacetimes in ddimensions. 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.
 Authors:

^{[1]};
^{[2]}
 Kutztown Univ., Kutztown, PA (United States)
 Pennsylvania State Univ., University Park, PA (United States)
 Publication Date:
 Grant/Contract Number:
 SC0010534
 Type:
 Published Article
 Journal Name:
 Nuclear Physics. B
 Additional Journal Information:
 Journal Volume: 904; Journal Issue: C; Journal ID: ISSN 05503213
 Publisher:
 Elsevier
 Research Org:
 Pennsylvania State Univ., University Park, PA (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 OSTI Identifier:
 1236905
 Alternate Identifier(s):
 OSTI ID: 1252957
Fernando, Sudarshan, and Gunaydin, Murat. Massless conformal fields, AdS(d+1)/CFTd higher spin algebras and their deformations. United States: N. p.,
Web. doi:10.1016/j.nuclphysb.2016.01.024.
Fernando, Sudarshan, & Gunaydin, Murat. Massless conformal fields, AdS(d+1)/CFTd higher spin algebras and their deformations. United States. doi:10.1016/j.nuclphysb.2016.01.024.
Fernando, Sudarshan, and Gunaydin, Murat. 2016.
"Massless conformal fields, AdS(d+1)/CFTd higher spin algebras and their deformations". United States.
doi:10.1016/j.nuclphysb.2016.01.024.
@article{osti_1236905,
title = {Massless conformal fields, AdS(d+1)/CFTd higher spin algebras and their deformations},
author = {Fernando, Sudarshan and Gunaydin, Murat},
abstractNote = {Here, we extend our earlier work on the minimal unitary representation of SO(d, 2)and its deformations for d=4, 5and 6to arbitrary dimensions d. We show that there is a onetoone correspondence between the minrep of SO(d, 2)and its deformations and massless conformal fields in Minkowskian spacetimes in ddimensions. 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.},
doi = {10.1016/j.nuclphysb.2016.01.024},
journal = {Nuclear Physics. B},
number = C,
volume = 904,
place = {United States},
year = {2016},
month = {2}
}