Quasiconformal Group Approach to Higher Spin Algebras, their Deformations and Supersymmetric Extensions
arXiv:1603.02359 · doi:10.1142/9789813144101_0010
Abstract
The quasiconformal method provides us with a unified approach to the construction of minimal unitary representations (minrep) of noncompact groups, their deformations as well as their supersymmetric extensions. We review the quasiconformal construction of the minrep of SO(d,2), its deformations and their applications to unitary realizations of AdS_{(d+1)}/CFT_d higher spin algebras and their deformations for arbitrary d and supersymmetric extensions for dimensions d less than seven. AdS_{(d+1)}/CFT_d higher spin algebras, their deformations and supersymmetric extensions are given by the enveloping algebras of the quasiconformal realizations of the minrep, its deformations and supersymmetric extensions, respectively, and are in one-to-one correspondence with massless conformal fields for arbitrary d and massless conformal supermultiplets for dimensions d less than seven.
36 pages; latex file; To appear in the "Proceedings of the International Workshop on Higher Spin Gauge Theories" , Singapore, November 4-6, 2015
References in corpus (6)
- Elements of Vasiliev theory
- On the Algebraic Structure of Higher-Spin Field Equations and New Exact Solutions
- Massless conformal fields, AdS_{d+1}/CFT_d higher spin algebras and their deformations
- The so(d+2,2) Minimal Representation and Ambient Tractors: the Conformal Geometry of Momentum Space
- SU(2) deformations of the minimal unitary representation of OSp(8*|2N) as massless 6D conformal supermultiplets
- Minimal unitary representation of 5d superconformal algebra F(4) and AdS_6/CFT_5 higher spin (super)-algebras