Twisted Flato-Fronsdal Theorem for Higher-Spin Algebras

TL;DR

This paper investigates the relationship between singleton and adjoint modules in higher-spin algebras using character methods, providing a heuristic symmetrization approach that accurately reproduces adjoint-module characters in various higher-spin gravity theories.

Contribution

Introduces a novel symmetrization-based formula linking singleton tensor products to adjoint modules in higher-spin algebras, validated across multiple models and dimensions.

Findings

The formula reproduces the adjoint-module character for type-A theories.

The approach works for high-order extensions and type-B theories.

Discusses implications of symmetrization in different models.

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.