(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, in contrast to the known flat space discontinuities for both systems. In an AdS background, unlike spin~2 where the limit m\to0 is the massless one, spin~3/2 masslessness'' requires m\to\sqrt{-\Lambda/3}, the supergravity value tuning the mass and cosmological constant that uniquely provides gauge invariance and two helicities. We find that continuity of the spin~3/2--mediated exchange amplitude can be regained in two massless’’ limits m\to0 and m\to\sqrt{-\Lambda/3}; only the latter corresponds to cosmological supergravity.