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.
Highlights
Recent years have seen a renewed interested in the challenge to extend the successes of the Bootstrap and the AdS/CFT paradigm to more general backgrounds, in particular those that are closer to real world
We study the consistency of the cubic couplings of amassless spinning field to two scalars in (d + 1)-dimensional de Sitter space
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 externalmassless field of arbitrary integer spin-J. 3-point Ward-Takahashi identities constrain the mass of the scalar fields to which amassless spin-J field can couple. 4-point Ward-Takahashi identities constrain the corresponding cubic couplings
Summary
In this case the Mellin-Barnes representation is not required to describe the correlator completely and the integrals can be lifted to give explicit closed form expressions for the three-point function of a (partially)massless field and two conformally coupled scalars. For a (most-likely) incomplete list see refs. [9, 10, 15, 16, 21, 24, 45, 48,49,50,51,52,53,54,55,56,57]
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