Skip to main content

Research Repository

Advanced Search

On the consistency of (partially-)massless matter couplings in de Sitter space

Sleight, Charlotte; Taronna, Massimo

On the consistency of (partially-)massless matter couplings in de Sitter space Thumbnail


Massimo Taronna


We study the consistency of the cubic couplings of a (partially-)massless spinning field to two scalars in (d + 1)-dimensional de Sitter space. Gauge invariance of observables with external (partially)-massless spinning fields translates into Ward-Takahashi identities on the boundary. Using the Mellin-Barnes representation for boundary correlators in momentum space, we give a systematic study of Ward-Takahashi identities for tree-level 3- and 4-point processes involving a single external (partially-)massless field of arbitrary integer spin-J. 3-point Ward-Takahashi identities constrain the mass of the scalar fields to which a (partially-)massless spin-J field can couple. 4-point Ward-Takahashi identities then constrain the corresponding cubic couplings. For massless spinning fields, we show that Weinberg’s flat space results carry over to (d+1)-dimensional de Sitter space: for spins J = 1, 2 gauge-invariance implies charge-conservation and the equivalence principle while, assuming locality, higher-spins J > 2 cannot couple consistently to scalar matter. This result also applies to anti-de Sitter space. For partially-massless fields, restricting for simplicity to those of depth-2, we show that there is no consistent coupling to scalar matter in local theories. Along the way we also give a detailed account of how contact amplitudes with and without derivatives are represented in the Mellin-Barnes representation. Various new explicit expressions for 3- and 4-point functions involving (partially-)massless fields and conformally coupled scalars in dS4 are given.


Sleight, C., & Taronna, M. (2021). On the consistency of (partially-)massless matter couplings in de Sitter space. Journal of High Energy Physics, 2021(10), Article 156 (2021).

Journal Article Type Article
Acceptance Date Sep 24, 2021
Online Publication Date Oct 19, 2021
Publication Date 2021
Deposit Date Jan 12, 2022
Publicly Available Date Jan 14, 2022
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2021
Issue 10
Article Number 156 (2021)


Published Journal Article (Advance online version) (961 Kb)

Publisher Licence URL

Copyright Statement
Advance online version This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

You might also like

Downloadable Citations