(Dis)continuities of Massless Limits in Spin 3/2-mediated Interactions and Cosmological Supergravity

We extend to its spin 3/2 supersymmetric partner the very recent demonstration that the massless limit of massive spin 2 exchange amplitudes can be made continuous in background AdS spaces. (It was shown long ago for both systems that discontinuities are unavoidable for the massless limit in flat backgrounds.) In an AdS background, unlike spin 2 where the limit $m \to 0$ is the massless one, spin 3/2 masslessness requires $m \to \sqrt{-\Lambda/3}$: the supergravity value tuning the mass and cosmological constant. We find that continuity of the spin 3/2-mediated exchange amplitude can be regained in two ``massless'' limits $m \to 0$ and $m \to \sqrt{-\Lambda/3}\$; only the latter corresponds to cosmological supergravity.