Singletons and their maximal symmetry algebras

Abstract

Singletons are those unitary irreducible modules of the Poincare or (anti) de Sitter group that can be lifted to unitary modules of the conformal group. Higher-spin algebras are the corresponding realizations of the universal enveloping algebra of the conformal algebra on these modules. These objects appear in a wide variety of areas of theoretical physics: AdS/CFT correspondence, electric-magnetic duality, higher-spin multiplets, infinite-component Majorana equations, higher-derivative symmetries, etc. Singletons and higher-spin algebras are reviewed through a list of their many equivalent definitions in order to approach them from various perspectives. The focus of this introduction is on the symmetries of a singleton: its maximal algebra and the manifest realization thereof.

34 pages, published (splitted into two distinct pieces) in the proceedings of the "7th spring school and workshop on quantum field theory & Hamiltonian systems" and of the "6th mathematical physics meeting: summer school and conference on modern mathematical physics", v2: references (and related comments) added, v3: typos corrected

References in corpus (4)

• A Fiber Approach to Harmonic Analysis of Unfolded Higher-Spin Field Equations
• Conformal theories including conformal gravity as gauge theories on the hypercone
• The so(d+2,2) Minimal Representation and Ambient Tractors: the Conformal Geometry of Momentum Space
• Generalized Symmetries of Massless Free Fields on Minkowski Space

Cited by in corpus (8)

• Eisenstein series and automorphic representations
• Multiparticle extension of the higher-spin algebra
• One-loop Test of Free SU(N) Adjoint Model Holography
• Supersymmetric Partially Massless Fields and Non-Unitary Superconformal Representations
• Saturating the unitarity bound in AdS/CFT_(AdS)
• $\mathcal{N}=2$ Supersymmetric Partially Massless Fields and Non-Unitary Superconformal Representations
• Extended hamiltonian action for arbitrary spin fields in flat and AdS spaces
• Conformal totally symmetric arbitrary spin fermionic fields