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Cubic interactions between the simplest mixed-symmetry gauge field andgravity are constructed in anti-de Sitter (AdS) and flat backgrounds.Nonabelian cubic interactions are obtained in AdS following variousperturbative methods including the Fradkin-Vasiliev construction, with andwithout Stueckelberg fields. The action that features the maximal number ofStueckelberg fields can be considered in the flat limit without loss ofphysical degrees of freedom. The resulting interactions in flat space arecompared with a classification of vertices obtained via the antifieldcohomological perturbative method. It is shown that the gauge algebra becomesabelian in the flat limit, in contrast to what happens for totally symmetricgauge fields in AdS.

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