Abstract
In this paper, we calculate higher point tree level vector amplitudes propagating in AdS4, or equivalently the dual boundary current correlators. We use bulk perturbation theory to compute tree level Witten diagrams. We show that when these amplitudes are written in momentum space, they reduce to relatively simple expressions. We explicitly compute four and five point correlators and also sketch a general strategy to compute the full six-point correlators.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
J. Penedones, TASI lectures on AdS/CFT, in the proceedingsof the Theoretical Advanced Study Institute in Elementary Particle Physics: New Frontiers in Fields and Strings (TASI 2015), June 1–26, Boulder, U.S.A. (2015), arXiv:1608.04948 [INSPIRE].
D. Poland, S. Rychkov and A. Vichi, The conformal bootstrap: theory, numerical techniques and applications, Rev. Mod. Phys. 91 (2019) 15002 [arXiv:1805.04405] [INSPIRE].
D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Comments on 4 point functions in the CFT/AdS correspondence, Phys. Lett. B 452 (1999) 61 [hep-th/9808006].
H. Liu and A.A. Tseytlin, On four point functions in the CFT/AdS correspondence, Phys. Rev. D 59 (1999) 086002 [hep-th/9807097].
D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Correlation functions in the CFT(d)/AdS(d+1) correspondence, Nucl. Phys. B 546 (1999) 96 [hep-th/9804058] [INSPIRE].
E. D’Hoker, D.Z. Freedman and L. Rastelli, AdS/CFT four point functions: how to succeed at z integrals without really trying, Nucl. Phys. B 562 (1999) 395 [hep-th/9905049] [INSPIRE].
E. D’Hoker et al., Graviton exchange and complete four point functions in the AdS/CFT correspondence, Nucl. Phys. B 562 (1999) 353 [hep-th/9903196] [INSPIRE].
J. Penedones, Writing CFT correlation functions as AdS scattering amplitudes, JHEP 03 (2011) 025 [arXiv:1011.1485] [INSPIRE].
M.F. Paulos, Towards Feynman rules for Mellin amplitudes, JHEP 10 (2011) 074 [arXiv:1107.1504] [INSPIRE].
G. Mack, D-dimensional conformal field theories with anomalous dimensions as dual resonance models, Bulg. J. Phys. 36 (2009) 214 [arXiv:0909.1024] [INSPIRE].
A.L. Fitzpatrick et al., A Natural Language for AdS/CFT Correlators, JHEP 11 (2011) 095 [arXiv:1107.1499] [INSPIRE].
S. Kharel and G. Siopsis, Tree-level correlators of scalar and vector fields in AdS/CFT, JHEP 11 (2013) 159 [arXiv:1308.2515] [INSPIRE].
A.L. Fitzpatrick and J. Kaplan, Analyticity and the holographic S-matrix, JHEP 10 (2012) 127 [arXiv:1111.6972] [INSPIRE].
A.L. Fitzpatrick and J. Kaplan, Unitarity and the holographic S-matrix, JHEP 10 (2012) 032 [arXiv:1112.4845] [INSPIRE].
M.S. Costa, V. Gonçalves and J. Penedones, Spinning AdS propagators, JHEP 09 (2014) 064 [arXiv:1404.5625] [INSPIRE].
S. Raju, BCFW for Witten diagrams, Phys. Rev. Lett. 106 (2011) 091601 [arXiv:1011.0780] [INSPIRE].
S. Raju, Four point functions of the stress tensor and conserved currents in AdS 4 /CFT 3, Phys. Rev. D 85 (2012) 126008 [arXiv:1201.6452] [INSPIRE].
S. Raju, New recursion relations and a flat space limit for AdS/CFT correlators, Phys. Rev. D 85 (2012) 126009 [arXiv:1201.6449] [INSPIRE].
S. Raju, Recursion relations for AdS/CFT correlators, Phys. Rev. D 83 (2011) 126002 [arXiv:1102.4724].
N. Arkani-Hamed and J. Maldacena, Cosmological collider physics, arXiv:1503.08043 [INSPIRE].
A. Bzowski, P. McFadden and K. Skenderis, Implications of conformal invariance in momentum space, JHEP 03 (2104) 111 [arXiv:1304.7760].
A. Bzowski, P. McFadden and K. Skenderis, Scalar 3-point functions in CFT: renormalisation, β-functions and anomalies, JHEP 03 (2016) 066 [arXiv:1510.08442] [INSPIRE].
A. Bzowski, P. McFadden and K. Skenderis, Evaluation of conformal integrals, JHEP 02 (2016) 068 [arXiv:1511.02357] [INSPIRE].
J.M. Maldacena, Non-Gaussian features of primordial fluctuations in single field inflationary models, JHEP 05 (2003) 013 [astro-ph/0210603] [INSPIRE].
J.M. Maldacena and G.L. Pimentel, On graviton non-Gaussianities during inflation, JHEP 09 (2011) 045 [arXiv:1104.2846] [INSPIRE].
R. Britto, F. Cachazo, B. Feng and E. Witten, Direct proof of tree-level recursion relation in Yang-Mills theory, Phys. Rev. Lett. 94 (2005) 181602 [hep-th/0501052] [INSPIRE].
E. Witten, Perturbative gauge theory as a string theory in twistor space, Commun. Math. Phys. 252 (2004) 189 [hep-th/0312171] [INSPIRE].
N. Arkani-Hamed, F. Cachazo and J. Kaplan, What is the simplest quantum field theory?, JHEP 09 (2010) 016 [arXiv:0808.1446] [INSPIRE].
N. Arkani-Hamed, F. Cachazo, C. Cheung and J. Kaplan, A Duality For The S Matrix, JHEP 03 (2010) 020 [arXiv:0907.5418] [INSPIRE].
N. Arkani-Hamed, F. Cachazo and C. Cheung, The Grassmannian origin of dual superconformal invariance, JHEP 03 (2010) 036 [arXiv:0909.0483].
H. Elvang and Y.T. Huang, Scattering amplitudes, arXiv:1308.1697.
C. Fronsdal, Elementary particles in a curved space. II, Phys. Rev. D 10 (1974) 589 [INSPIRE].
L.J. Dixon, Calculating scattering amplitudes efficiently, talk given at the QCD and beyond. Theoretical Advanced Study Institute in Elementary Particle Physics (TASI-95), June 4–30, Boulder, U.S.A. (1995), hep-ph/9601359 [INSPIRE].
D. Anninos, T. Anous, D.Z. Freedman and G. Konstantinidis, Late-time Structure of the Bunch-Davies de Sitter Wavefunction, JCAP 11 (2015) 048 [arXiv:1406.5490] [INSPIRE].
N. Arkani-Hamed, P. Benincasa and A. Postnikov, Cosmological polytopes and the wavefunction of the universe, arXiv:1709.02813 [INSPIRE].
C. Chowdhury and S. Kharel, All recursion relation for dual CFT correlators, in preparation.
K. Risager, A direct proof of the CSW rules, JHEP 12 (2005) 003 [hep-th/0508206].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1810.12459
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Albayrak, S., Kharel, S. Towards the higher point holographic momentum space amplitudes. J. High Energ. Phys. 2019, 40 (2019). https://doi.org/10.1007/JHEP02(2019)040
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2019)040