KLT-like behaviour of inflationary graviton correlators

In this follow up paper, we calculate higher point tree level graviton Witten diagrams in AdS 4 via bulk perturbation theory. We show that by rearranging the bulk to bulk graviton propagators, the calculations effectively reduce to the computation of a scalar factor. Analogous to the amplitudes for vector boson interactions we computed in the previous paper, scalar factors for the graviton exchange diagrams also become relatively simple when written in momentum space. We explicitly calculate higher point correlators and discuss how this momentum space formalism makes flat space and collinear limits simpler.

Section: Resultsmentioning

confidence: 99%

Towards the higher point holographic momentum space amplitudes. Part II. Gravitons

Albayrak

Kharel

2019

“…A simple example is the conformally coupled scalar, µ = 1 2 , which pinches the integration contour when d (n − 2) − n = 0. 15 With the above regularisation, the integral (3.24) Figure 5: Poles of the Mellin representation for the conformal structure (3.24) when the n-th scalar does not lie on the Principal Series, ν n = iµ with µ ∈ R. For ease of presentation, we display the n = 3 case. As µ varies, the poles of Γ d 4 ± iνn 2 − s (in blue) move along the real axis while the poles of Γ (2s − 1) (in red) remain fixed.…”

Section: N-point Contact Diagrams With Conformally Coupled Scalarsmentioning

confidence: 99%

A Mellin space approach to cosmological correlators

Sleight

2020

162

193

We propose a Mellin space approach to the evaluation of late-time momentumspace correlation functions of quantum fields in (d + 1)-dimensional de Sitter space. The Mellin-Barnes representation makes manifest the analytic structure of late-time correlators and, more generally, provides a convenient general d framework for the study of conformal correlators in momentum space. In this work we focus on tree-level correlation functions of general scalars as a prototype, including n-point contact diagrams and 4-point exchanges. For generic scalars, both the contact and exchange diagrams are given by (generalised) Hypergeometric functions, which reduce to existing expressions available in the literature for d = 3 and external scalars which are either simultaneously conformally coupled or massless. This approach can also be used for the perturbative bulk evaluation of momentum space boundary correlators in (d + 1)-dimensional anti-de Sitter space (Witten diagrams).

“…Recent discussions at the level of the 4-point function include [28][29][30][31][32][33]. Moreover, KLT-like relations for the inflationary graviton 4-point function were identified in [34]. Alternatively, the connection with scattering amplitudes can be used to compute higher-point AdS Witten diagrams via an analogue of BCFW recursion [16,[35][36][37][38].…”

Section: Contentsmentioning

confidence: 99%

Double copy structure of CFT correlators

Farrow

Lipstein

McFadden

2019

124

119

We consider the momentum-space 3-point correlators of currents, stress tensors and marginal scalar operators in general odd-dimensional conformal field theories. We show that the flat space limit of these correlators is spanned by gauge and gravitational scattering amplitudes in one higher dimension which are related by a double copy. Moreover, we recast three-dimensional CFT correlators in terms of tree-level Feynman diagrams without energy conservation, suggesting double copy structure beyond the flat space limit.