Twisted Flato-Fronsdal Theorem for Higher-Spin Algebras

Understand

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.