Non-abelian cubic vertices for higher-spin fields in anti-de Sitter space

TL;DR

This paper constructs all non-abelian cubic interaction vertices for symmetric higher-spin gauge fields in anti-de Sitter space using the Fradkin-Vasiliev method, revealing their algebraic structure and relation to flat space deformations.

Contribution

It provides a complete classification of non-abelian cubic vertices for higher-spin fields in AdS space and explores their algebraic properties and relations to flat space results.

Findings

Number of vertices given by tensor-product multiplicity

Relation between AdS vertices and flat space deformations

Discussion of algebraic properties and uniqueness of higher-spin algebras

Abstract

We use the Fradkin-Vasiliev procedure to construct the full set of non-abelian cubic vertices for totally symmetric higher spin gauge fields in anti-de Sitter space. The number of such vertices is given by a certain tensor-product multiplicity. We discuss the one-to-one relation between our result and the list of non-abelian gauge deformations in flat space obtained elsewhere via the cohomological approach. We comment about the uniqueness of Vasiliev's simplest higher-spin algebra in relation with the (non)associativity properties of the gauge algebras that we classified. The gravitational interactions for (partially)-massless (mixed)-symmetry fields are also discussed. We also argue that those mixed-symmetry and/or partially-massless fields that are described by one-form connections within the frame-like approach can have nonabelian interactions among themselves and again the number of nonabelian vertices should be given by tensor product multiplicities.