Massless conformal fields, AdS(d+1)/CFTd higher spin algebras and their deformations
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2016-03-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321316000341 |
| _version_ | 1818262884989272064 |
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| author | Sudarshan Fernando Murat Günaydin |
| author_facet | Sudarshan Fernando Murat Günaydin |
| author_sort | Sudarshan Fernando |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-12T19:10:13Z |
| format | Article |
| id | doaj.art-2177db1b25074afd87a9b08d9426dfc0 |
| institution | Directory Open Access Journal |
| issn | 0550-3213 1873-1562 |
| language | English |
| last_indexed | 2024-12-12T19:10:13Z |
| publishDate | 2016-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-2177db1b25074afd87a9b08d9426dfc02022-12-22T00:14:52ZengElsevierNuclear Physics B0550-32131873-15622016-03-01904C49452610.1016/j.nuclphysb.2016.01.024Massless conformal fields, AdS(d+1)/CFTd higher spin algebras and their deformationsSudarshan Fernando0Murat Günaydin1Physical Sciences Department, Kutztown University, Kutztown, PA 19530, USAInstitute for Gravitation and the Cosmos, Physics Department, Pennsylvania State University, University Park, PA 16802, USAWe 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.http://www.sciencedirect.com/science/article/pii/S0550321316000341 |
| spellingShingle | Sudarshan Fernando Murat Günaydin Massless conformal fields, AdS(d+1)/CFTd higher spin algebras and their deformations Nuclear Physics B |
| title | Massless conformal fields, AdS(d+1)/CFTd higher spin algebras and their deformations |
| title_full | Massless conformal fields, AdS(d+1)/CFTd higher spin algebras and their deformations |
| title_fullStr | Massless conformal fields, AdS(d+1)/CFTd higher spin algebras and their deformations |
| title_full_unstemmed | Massless conformal fields, AdS(d+1)/CFTd higher spin algebras and their deformations |
| title_short | Massless conformal fields, AdS(d+1)/CFTd higher spin algebras and their deformations |
| title_sort | massless conformal fields ads d 1 cftd higher spin algebras and their deformations |
| url | http://www.sciencedirect.com/science/article/pii/S0550321316000341 |
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