Towards the higher point holographic momentum space amplitudes

Albayrak, Soner; Kharel, Savan

doi:10.1007/jhep02(2019)040

Cited by 55 publications

(97 citation statements)

References 36 publications

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“…However, previous works have largely focused on conformal theories and using a representation in position space, or Mellin transforms that take advantage of conformal symmetry [31][32][33][34]. In some cases, but still restricted to conformal theories, correlators in momentum space have also been studied; for recent works, see [35][36][37].…”

Section: Discussionmentioning

confidence: 99%

Scattering length from holographic duality

2020

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Interesting theories with short range interactions include QCD in the hadronic phase and cold atom systems. The scattering length in two-to-two elastic scattering process captures the most elementary features of the interactions, such as whether they are attractive or repulsive. However, even this basic quantity is notoriously difficult to compute from first principles in strongly coupled theories. We present a method to compute the two-to-two amplitudes and the scattering length using the holographic duality. Our method is based on the identification of the residues of Green's functions in the gravity dual with the amplitudes in the field theory. To illustrate the method we compute a contribution to the scattering length in a hard wall model with a quartic potential and find a constraint on the scaling dimension of a scalar operator ∆ > d/4. For d < 4 this is more stringent than the unitarity constraint and may be applicable to an extended family of large-N theories with a discrete spectrum of massive states. We also argue that for scalar potentials with polynomial terms of order K, a constraint more restrictive than the unitarity bound will appear for d < 2K/(K − 2).

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Section: Discussionmentioning

confidence: 99%

Scattering length from holographic duality

2020

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“…To date there are only a handful of works on momentum space approaches to Witten diagrams see e.g. [41,42,[125][126][127][128][129][130].…”

Section: Four-point Exchange Witten Diagram For Generic Scalar Fieldsmentioning

confidence: 99%

Bootstrapping inflationary correlators in Mellin space

Sleight

Taronna

2020

J. High Energ. Phys.

190

293

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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.

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“…In this section we provide a brief review of momentum space bulk perturbation theory. We refer reader interested in scalars and vector bosons to [54] and the references therein; in this follow-up paper, we will present a very succinct overview with an emphasis on the gravitons.…”

Section: Review: Ads Momentum Space Perturbation Theorymentioning

confidence: 99%

“…In this paper, we will stick to spacelike momenta, i.e. k 2 = k 2 , as was done in [54]: one can analytically continue to timelike momenta, however the bulk to boundary propagators need to be modified accordingly [41].…”

Section: Review: Ads Momentum Space Perturbation Theorymentioning

confidence: 99%

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