New relation for Witten diagrams

Albayrak, Soner; Chowdhury, Chandramouli; Kharel, Savan

doi:10.1007/jhep10(2019)274

Cited by 59 publications

(58 citation statements)

References 47 publications

(59 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…9 Apart from its physical significance, we focus on AdS 4 also because Bessel functions simplify for half integer arguments; hence the calculations are relatively easier for AdS 2þ2n . This motivation was also used in previous similar work [59,60,62], where the calculation of graviton amplitudes in [60] is actually quite similar to the computation at hand. Specially, one can write the graviton propagators in AdS dþ1 as…”

Section: Example: Minimally Coupled Scalars In Adsmentioning

confidence: 88%

“…In this section, we will review the basics of our framework and specifics regarding the scalars. For similar reviews in the context of gauge fields and gravitons, see [59,60,62].…”

Section: B Review Of Momentum Space Toolkit In Adsmentioning

confidence: 99%

“…Such an algorithm is discussed in [62] where the authors refer to the additive property of vertices, enabling them to work at the level of truncated diagrams and compute amplitudes directly via algebraic means. This is possible, as they argue, because the gluon propagators in AdS 4 are simply exponentials and there is a nice cancellation between the volume factor z −d−1 and the vertex factor z 4 in AdS 4 .…”

Section: ð3:4þmentioning

confidence: 99%

“…So we arrive at the conclusion that one can reduce the integrations to algebraic calculations for scalars with conformal symmetry in any dimension, analogous to gluons in AdS 4 . 16,17 Let us quickly review the algorithm to compute the Witten As we explained in footnote 9, we treat the overall kdependence as normalization which we chose for the conformally coupled scalars in a consistent fashion with the similar work in [35,36,62]. 16 One can in fact still use the algorithm for conformally coupled scalars with n ≠ n c with appropriate modification.…”

Section: ð3:4þmentioning

confidence: 99%

“…The momentum space formalism for AdS calculations can be upgraded with a new algorithm developed by Arkani-Hamed, Benincasa, and Postnikov in [61] where they investigate the wave function of the Universe in de Sitter background. Indeed, it was realized in [62] that the computation of gluon Witten diagrams in AdS 4 can actually use the same combinatorial relations developed in [61] if it is written in momentum space. This correspondence allowed the authors to compute any tree level gluon exchange diagram algebraically, without having to do any explicit bulk integrations.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Study of momentum space scalar amplitudes in AdS spacetime

2020

Self Cite

View full text Add to dashboard Cite

In this paper, we explore momentum space approach to computing scalar amplitudes in anti-de Sitter (AdS) space. We show that the algorithm derived by Arkani-Hamed, Benincasa, and Postnikov for cosmological wave functions can be straightforwardly adopted for AdS transition amplitudes in momentum space, allowing one to bypass bulk point integrations. We demonstrate the utility of this approach in AdS by presenting several explicit results both at tree and loop level.

show abstract

Section: Example: Minimally Coupled Scalars In Adsmentioning

confidence: 88%

“…In this section, we will review the basics of our framework and specifics regarding the scalars. For similar reviews in the context of gauge fields and gravitons, see [59,60,62].…”

Section: B Review Of Momentum Space Toolkit In Adsmentioning

confidence: 99%

Section: ð3:4þmentioning

confidence: 99%

Section: ð3:4þmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Study of momentum space scalar amplitudes in AdS spacetime

2020

Self Cite

View full text Add to dashboard Cite

show abstract

A Mellin space approach to cosmological correlators

Sleight

2020

J. High Energ. Phys.

154

193

View full text Add to dashboard Cite

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).

show abstract

Towards Feynman rules for conformal blocks

Hoback

Parikh

2021

J. High Energ. Phys.

View full text Add to dashboard Cite

We conjecture a simple set of “Feynman rules” for constructing n-point global conformal blocks in any channel in d spacetime dimensions, for external and exchanged scalar operators for arbitrary n and d. The vertex factors are given in terms of Lauricella hypergeometric functions of one, two or three variables, and the Feynman rules furnish an explicit power-series expansion in powers of cross-ratios. These rules are conjectured based on previously known results in the literature, which include four-, five- and six-point examples as well as the n-point comb channel blocks. We prove these rules for all previously known cases, as well as two new ones: the seven-point block in a new topology, and all even-point blocks in the “OPE channel.” The proof relies on holographic methods, notably the Feynman rules for Mellin amplitudes of tree-level AdS diagrams in a scalar effective field theory, and is easily applicable to any particular choice of a conformal block beyond those considered in this paper.

show abstract

New relation for Witten diagrams

Cited by 59 publications

References 47 publications

Study of momentum space scalar amplitudes in AdS spacetime

Study of momentum space scalar amplitudes in AdS spacetime

A Mellin space approach to cosmological correlators

Towards Feynman rules for conformal blocks

Contact Info

Product

Resources

About