On the consistency of (partially-)massless matter couplings in de Sitter space

Understand

We study the consistency of the cubic couplings of a (partially-)massless spinning field to two scalars in $\left(d+1\right)$-dimensional de Sitter space.

• Gauge invariance of observables with external (partially)-massless spinning fields translates into Ward-Takahashi identities on the boundary.
• Using the Mellin-Barnes representation for boundary correlators in momentum space, we give a systematic study of Ward-Takahashi identities for tree-level 3- and 4-point processes involving a single external (partially-)massless field of arbitrary integer spin-$J$.
• 3-point Ward-Takahashi identities constrain the mass of the scalar fields to which a (partially-)massless spin-$J$ field can couple.