Twisted Flato-Fronsdal Theorem for Higher-Spin Algebras

Abstract

We explore the relation between the singleton and adjoint modules of higher-spin algebras via so(2,d) characters. In order to relate the tensor product of the singleton and its dual to the adjoint module, we consider a heuristic formula involving symmetrization over the variables of the character. We show that our formula reproduces correctly the adjoint-module character for type-A (and its high-order extensions) and type-B higher-spin gravity theories in any dimension. Implications and subtleties of this symmetrization prescription in other models are discussed.

arXiv comment50 pages, 2 figures; v2: references added, typos corrected and discussion concerning the proposed formula extended

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