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

TL;DR

This paper investigates the continuity of massless limits in spin 3/2 interactions within AdS spaces, revealing that only a specific limit aligns with cosmological supergravity, contrasting flat space discontinuities.

Contribution

It extends the analysis of massless limits from spin 2 to spin 3/2 in AdS backgrounds, identifying conditions for continuous amplitudes and linking them to cosmological supergravity.

Findings

Continuity of spin 3/2 exchange amplitudes in AdS can be achieved in two limits.

Only the limit m→√(-Λ/3) corresponds to cosmological supergravity.

Flat space limits exhibit discontinuities for spin 3/2 interactions.

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{-\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.