Consistent Couplings between a Massive Spin-3/2 Field and a Partially Massless Spin-2 Field

Abstract

We revisit the problem of constructing consistent interactions between a massive spin-3/2 field and a partially massless graviton in four-dimensional (anti) de Sitter (A)dS4 spacetime. We use the Stueckelberg formulation of the action principle for these fields and find two non-trivial cubic vertices with less than two derivatives when moving to the unitary gauge. One of the vertices is reminiscent of the minimal coupling of the massive spin-3/2 field to gravity, except that now the graviton is partially massless.