Consistent couplings between a massive spin-3/2 field and a partially massless spin-2 field

TL;DR

This paper explores consistent interaction vertices between a massive spin-3/2 field and a partially massless spin-2 field in (A)dS space, identifying two non-trivial cubic couplings with fewer than two derivatives.

Contribution

It introduces two new cubic interaction vertices between these fields using the Stueckelberg approach, expanding understanding of their coupling in (A)dS spacetime.

Findings

Identified two non-trivial cubic vertices with less than two derivatives.

One vertex resembles minimal coupling but involves a partially massless graviton.

Results contribute to the theory of higher-spin field interactions in curved spacetime.

Abstract

We revisit the problem of constructing consistent interactions between a massive spin-3/2 field and a partially massless graviton in four-dimensional (A)dS 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 going 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.