Gravitational cubic interactions for a simple mixed-symmetry gauge field in AdS and flat backgrounds

TL;DR

The paper constructs gravitational cubic interactions between the simplest mixed-symmetry gauge field and gravity in both $AdS_d$ and flat backgrounds. Non-Abelian cubic interactions are realized in $AdS_d$ via perturbative methods, including the Fradkin-Vasiliev construction, with and without Stueckelberg fields. The flat limit is explored by taking the action with the maximal number of Stueckelberg fields, allowing a well-defined flat-space limit, and the resulting vertices are compared with those classified by antifield cohomological perturbation theory. A key finding is that the gauge algebra becomes abelian in the flat limit, in contrast to the non-Abelian structure for totally symmetric higher-spin fields in $AdS_d$.

Abstract

Cubic interactions between the simplest mixed-symmetry gauge field and gravity are constructed in anti-de Sitter (AdS) and flat backgrounds. Nonabelian cubic interactions are obtained in AdS following various perturbative methods including the Fradkin-Vasiliev construction, with and without Stueckelberg fields. The action that features the maximal number of Stueckelberg fields can be considered in the flat limit without loss of physical degrees of freedom. The resulting interactions in flat space are compared with a classification of vertices obtained via the antifield cohomological perturbative method. It is shown that the gauge algebra becomes abelian in the flat limit, in contrast to what happens for totally symmetric gauge fields in AdS.