Quasiconformal Group Approach to Higher Spin Algebras, Their Deformations and Supersymmetric Extensions

DOI10.1142/9789813144101_0010zbMATH Open1359.81162arXiv1603.02359OpenAlexW2293579419MaRDI QIDQ2973049

Publication date: 31 March 2017

Published in: Higher Spin Gauge Theories (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1603.02359

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Supersymmetric field theories in quantum mechanics (81T60) Quantum field theory on curved space or space-time backgrounds (81T20) Applications of Lie groups to the sciences; explicit representations (22E70) Finite-dimensional groups and algebras motivated by physics and their representations (81R05)