On massive higher spins and gravity. Part III. Spin 7/2

A bstract In this paper, we extend our previous results on the gravitational interactions for massive spin 5/2 particles and spin 3 particles to massive spin 7/2, including its massless and partially massless limits. These results share some common features, such as a non-singular massless limit in AdS and a flat limit for non-zero masses, as well as a singularity at the points corresponding to the boundary of the unitary forbidden region. At the same time, these results allow us to suggest what the structure of non-minimal interactions for arbitrary spins looks like. Another subject of interest is the Skvortsov-Vasiliev formalism for describing free partially massless fields. This formalism has been very useful in our research, but our examples have shown that the application of the Fradkin-Vasiliev formalism for constructing interactions based on such description does not always lead to the correct results.