(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→0 is the massless one, spin-3/2 "masslessness" requires m → √-Λ / 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→0 and m → √-Λ/3; only the latter corresponds to cosmological supergravity.