(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.