Singletons and their maximal symmetry algebras

Details Singletons and their maximal symmetry algebras Singletons and their maximal symmetry algebras

2011-11-19

arxiv.org/abs/1111.4554v2

Physics

Mathematical Physics

34 pages, published (splitted into two distinct pieces) in the proceedings of the "7th spring school and workshop on quantum f

Scientific paper

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.

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