Abstract
Cubic interactions between the simplest mixed-symmetry gauge field and gravity are constructed in anti-de Sitter (AdS) and flat backgrounds. Non-Abelian cubic interactions are obtained in AdS following various perturbative methods including the Fradkin–Vasiliev construction, with and without Stückelberg fields. The action that features the maximal number of Stückelberg 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.
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