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

TL;DR

This paper reviews a unified quasiconformal approach to constructing minimal unitary representations of noncompact groups, their deformations, and supersymmetric extensions, with applications to higher spin algebras in AdS/CFT contexts across various dimensions.

Contribution

It introduces a quasiconformal method for constructing and analyzing higher spin algebras and their supersymmetric extensions in a unified framework.

Findings

Constructs minimal unitary representations of SO(d,2).

Relates higher spin algebras to enveloping algebras of quasiconformal realizations.

Connects these algebras to massless conformal fields and supermultiplets.

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.