Higher Spin Superalgebras in any Dimension and their Representations
| dc.creator | Vasiliev, M. A. | |
| dc.date | 2004-04-19 | |
| dc.date | 2005-02-08 | |
| dc.date.accessioned | 2026-07-07T10:49:53Z | |
| dc.date.available | 2026-07-07T10:49:53Z | |
| dc.description | Fock module realization for the unitary singleton representations of the $d-1$ dimensional conformal algebra $o(d-1,2)$, which correspond to the spaces of one-particle states of massless scalar and spinor in $d-1$ dimensions, is given. The pattern of the tensor product of a pair of singletons is analyzed in any dimension. It is shown that for $d>3$ the tensor product of two boson singletons decomposes into a sum of all integer spin totally symmetric massless representations in $AdS_d$, the tensor product of boson and fermion singletons gives a sum of all half-integer spin symmetric massless representations in $AdS_d$, and the tensor product of two fermion singletons in $d>4$ gives rise to massless fields of mixed symmetry types in $AdS_d$ depicted by Young tableaux with one row and one column together with certain totally antisymmetric massive fields. In the special case of $o(2,2)$, tensor products of 2d massless scalar and/or spinor modules contain infinite sets of 2d massless conformal fields of different spins. The obtained results extend the 4d result of Flato and Fronsdal \cite{FF} to any dimension and provide a nontrivial consistency check for the recently proposed higher spin model in $AdS_d$ \cite{d}. We define a class of higher spin superalgebras which act on the supersingleton and higher spin states in any dimension. For the cases of $AdS_3$, $AdS_4$, and $AdS_5$ the isomorphisms with the higher spin superalgebras defined earlier in terms of spinor generating elements are established. | |
| dc.description | LaTeX, 53 pages, no figures; v2: 54 pages, notations for higher spin algeras are simplified, a comment on tensor products of 2d massless fields and references added, typos corrected; v3: references added, typos corrected; v4: references added, notation simplified, clarification on finite dimensional subsuperalgebras of higher spin superalgebras added in section 5. The version published in JHEP | |
| dc.identifier | https://arxiv.org/abs/hep-th/0404124 | |
| dc.identifier | http://arxiv.org/abs/hep-th/0404124 | |
| dc.identifier | JHEP0412:046,2004 | |
| dc.identifier | doi:10.1088/1126-6708/2004/12/046 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/184370 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Higher Spin Superalgebras in any Dimension and their Representations | |
| dc.type | text |