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

TL;DR

This work studies the continuity of massless limits for spin-3/2 mediated interactions in AdS, extending the known spin-2 flat-space discontinuity and identifying $m^2=-\Lambda/3$ as the gauge-invariant, cosmological-supergravity point. It computes the one-particle exchange amplitude between covariantly conserved currents using the Rarita–Schwinger Lagrangian in AdS and half-integer Lichnerowicz operators, demonstrating poles cancel and decompositions into TT and gamma-trace sectors. Two limiting paths are analyzed: a de Sitter-like limit $m\to0$, where continuity depends on the order of limits and yields prefactors that can be $1/3$ or $1/2$, and a cosmological-supergravity limit $m\to\sqrt{-\Lambda/3}$ with a modified current conservation law that yields a smooth AdS supergravity amplitude. After taking $\Lambda\to0$, the cosmological limit reduces to the standard massless flat-space result with a $1/2$ prefactor, confirming a unique, continuous connection to Minkowski space for the properly tuned limit.

Abstract

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{-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\to0 and m\to\sqrt{-Λ/3}; only the latter corresponds to cosmological supergravity.