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

Sleight, Charlotte; Taronna, Massimo

Abstract

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.

Citation

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). https://doi.org/10.1007/jhep10%282021%29156

• 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
• Electronic ISSN: 1029-8479
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2021
• Issue: 10
• Article Number: 156 (2021)
• DOI: https://doi.org/10.1007/jhep10%282021%29156
• Public URL: https://durham-repository.worktribe.com/output/1217382