On cubic AdS interactions of mixed-symmetry higher spins

TL;DR

The paper tackles the problem of constructing consistent cubic AdS interactions for massless mixed-symmetry higher-spin fields, focusing on two-family representations and the TT sector. It recasts the Noether consistency condition into a system of linear PDEs for the ambient-space cubic vertex, which can be solved for given spin assignments. The analysis reveals a Fradkin-Vasiliev–like structure where the highest-derivative part of the vertex is supplemented by lower-derivative AdS-tail terms, with gauge-content constrained by the BMV pattern; a full Stückelberg analysis is reserved for future work. A concrete example for the hook-type case {2,1}-1-1 shows the TT system selecting a unique three-derivative coupling dressed by an AdS tail after projecting onto the appropriate Young tableau, illustrating the method and its on-shell content.

Abstract

The problem of finding consistent cubic AdS interactions of massless mixed-symmetry higher-spin fields is recast into a system of partial differential equations that can be solved for given spins of the particles entering the cubic vertices. For simplicity, we consider fields with two families of indices for which some examples of interactions are explicitly discussed.