Partially massless spin 5/2 and supersymmetry

We elaborate on the partially massless spin 5/2 supermultiplet, which contains partially massless spin 5/2, massless and partially massless spin 2, as well as massless spin 3/2. We consider the global supertransformations connecting partially massless spin 5/2 to its two possible superpartners, massless and partially massless spin 2, and make them local by switching the interaction with the massless gravitino. We use a frame-like gauge-invariant formalism to describe free fields and the Fradkin-Vasiliev formalism to construct interactions, Due to the presence of the Stueckelberg fields in the gauge-invariant description of massive and partially massless fields, we face ambiguities related to field redefinitions. We use this freedom to simplify calculations. At the same time, we demonstrate how these ambiguities can be resolved using unfolded equations.