A Mellin space approach to cosmological 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

“…We note that, while conformal symmetry fixes the location of the poles in the Mellin integrand, the zeros, encoded in the sine function in (3.12), are fixed by the early time boundary conditions (Bunch-Davis in our case). The expression (3.12) is also obtained by simply evaluating the late-time correlator directly in de Sitter space using the Mellin-Barnes representation for the propagators [44]. Here, we directly evaluated the Fourier transform of the known result [99,100] for tree-level three-point Witten diagrams of scalar fields in Euclidean anti-de Sitter space (which is most naturally given by a Mellin-Barnes integral) and applying the dictionary spelled out in §2.5 to each propagator at the level of the Mellin integrand to obtain the corresponding late-time correlator in de Sitter space.…”

Section: General External Scalarsmentioning

confidence: 99%

Bootstrapping inflationary correlators in Mellin space

Sleight

Taronna

2020

Self Cite

190

293

We develop a Mellin space approach to boundary correlation functions in anti-de Sitter (AdS) and de Sitter (dS) spaces. Using the Mellin-Barnes representation of correlators in Fourier space, we show that the analytic continuation between AdS d+1 and dS d+1 is encoded in a collection of simple relative phases. This allows us to determine the late-time tree-level three-point correlators of spinning fields in dS d+1 from known results for Witten diagrams in AdS d+1 by multiplication with a simple trigonometric factor. At four point level, we show that Conformal symmetry fixes exchange four-point functions both in AdS d+1 and dS d+1 in terms of the dual Conformal Partial Wave (which in Fourier space is a product of boundary three-point correlators) up to a factor which is determined by the boundary conditions. In this work we focus on late-time four-point correlators with external scalars and an exchanged field of integer spin-. The Mellin-Barnes representation makes manifest the analytic structure of boundary correlation functions, providing an analytic expression for the exchange four-point function which is valid for general d and generic scaling dimensions, in particular massive, light and (partially-)massless fields. It moreover naturally identifies boundary correlation functions for generic fields with multivariable Meijer-G functions. When d = 3 we reproduce existing explicit results available in the literature for external conformally coupled and massless scalars. From these results, assuming the weak breaking of the de Sitter isometries, we extract the corresponding correction to the inflationary three-point function of general external scalars induced by a general spin-field at leading order in slow roll. These results provide a step towards a more systematic understanding of de Sitter observables at tree level and beyond using Mellin space methods.

“…More recently, Refs. [42,43] developed a Mellin representation of exchange diagrams on (anti-)de Sitter space in momentum space for external scalars with arbitrary mass. It would be interesting to explore the relation of these works with ours.…”

Section: Resultsmentioning

confidence: 99%

Momentum space approach to crossing symmetric CFT correlators. Part II. General spacetime dimension

Isono

Noumi

Shiu

2019

Our previous work [1] constructed, in three-dimensional momentum space, a manifestly crossing symmetric basis for scalar conformal four-point functions, based on the factorization property proposed by Polyakov. This work extends this construction to general dimensional conformal field theory. To facilitate the treatment of symmetric traceless tensors, we exploit techniques of spherical harmonics in general dimensions.