Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-04-19
JHEP0412:046,2004
Physics
High Energy Physics
High Energy Physics - Theory
LaTeX, 53 pages, no figures; v2: 54 pages, notations for higher spin algeras are simplified, a comment on tensor products of 2
Scientific paper
10.1088/1126-6708/2004/12/046
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.
No associations
LandOfFree
Higher Spin Superalgebras in any Dimension and their Representations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Higher Spin Superalgebras in any Dimension and their Representations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Higher Spin Superalgebras in any Dimension and their Representations will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-382409