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

TL;DR

This paper constructs cubic gravitational interactions for a simple mixed-symmetry gauge field in AdS and flat spaces, revealing differences in gauge algebra behavior between these backgrounds.

Contribution

It introduces new cubic interaction vertices for mixed-symmetry gauge fields in both AdS and flat spaces, utilizing various perturbative methods including Fradkin-Vasiliev construction.

Findings

Nonabelian interactions are constructed in AdS.

In flat space, the gauge algebra becomes abelian.

Interactions in flat space match antifield cohomological classifications.

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.