Abstract
We present the computation of all the correlators of 1/2-BPS operators in \( \mathcal{N}=4 \) SYM with weights up to 8 as well as some very high-weight correlation functions from the effective supergravity action. The computation is done by implementing the recently developed simplified algorithm in combination with the harmonic polynomial formalism. We provide a database of these results attached to this publication and additionally check for almost all of the functions in this database that they agree with the conjecture on their Mellin-space form.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
L. Rastelli and X. Zhou, Mellin amplitudes for AdS 5 × S 5, Phys. Rev. Lett. 118 (2017) 091602 [arXiv:1608.06624] [INSPIRE].
L. Rastelli and X. Zhou, How to succeed at holographic correlators without really trying, JHEP 04 (2018) 014 [arXiv:1710.05923] [INSPIRE].
F.A. Dolan, M. Nirschl and H. Osborn, Conjectures for large N superconformal N = 4 chiral primary four point functions, Nucl. Phys. B 749 (2006) 109 [hep-th/0601148] [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].
G. Arutyunov and S. Frolov, Four point functions of lowest weight CPOs in N = 4 SYM(4) in supergravity approximation, Phys. Rev. D 62 (2000) 064016 [hep-th/0002170] [INSPIRE].
G. Arutyunov, F.A. Dolan, H. Osborn and E. Sokatchev, Correlation functions and massive Kaluza-Klein modes in the AdS/CFT correspondence, Nucl. Phys. B 665 (2003) 273 [hep-th/0212116] [INSPIRE].
G. Arutyunov and E. Sokatchev, On a large N degeneracy in N = 4 SYM and the AdS/CFT correspondence, Nucl. Phys. B 663 (2003) 163 [hep-th/0301058] [INSPIRE].
L. Berdichevsky and P. Naaijkens, Four-point functions of different-weight operators in the AdS/CFT correspondence, JHEP 01 (2008) 071 [arXiv:0709.1365] [INSPIRE].
L.I. Uruchurtu, Four-point correlators with higher weight superconformal primaries in the AdS/CFT Correspondence, JHEP 03 (2009) 133 [arXiv:0811.2320] [INSPIRE].
L.I. Uruchurtu, Next-next-to-extremal four point functions of N = 4 1/2 BPS operators in the AdS/CFT correspondence, JHEP 08 (2011) 133 [arXiv:1106.0630] [INSPIRE].
G. Arutyunov, S. Frolov, R. Klabbers and S. Savin, Towards 4-point correlation functions of any \( \frac{1}{2} \) -BPS operators from supergravity, JHEP 04 (2017) 005 [arXiv:1701.00998] [INSPIRE].
G. Arutyunov, R. Klabbers and S. Savin, Four-point functions of all-different-weight chiral primary operators in the supergravity approximation, JHEP 09 (2018) 023 [arXiv:1806.09200] [INSPIRE].
L.F. Alday and A. Bissi, Loop corrections to supergravity on AdS 5 × S 5, Phys. Rev. Lett. 119 (2017) 171601 [arXiv:1706.02388] [INSPIRE].
F. Aprile, J.M. Drummond, P. Heslop and H. Paul, Unmixing supergravity, JHEP 02 (2018) 133 [arXiv:1706.08456] [INSPIRE].
F. Aprile, J.M. Drummond, P. Heslop and H. Paul, Loop corrections for Kaluza-Klein AdS amplitudes, JHEP 05 (2018) 056 [arXiv:1711.03903] [INSPIRE].
F. Aprile, J. Drummond, P. Heslop and H. Paul, The double-trace spectrum of N = 4 SYM at strong coupling, arXiv:1802.06889 [INSPIRE].
F.A. Dolan and H. Osborn, Conformal partial waves and the operator product expansion, Nucl. Phys. B 678 (2004) 491 [hep-th/0309180] [INSPIRE].
M. Nirschl and H. Osborn, Superconformal Ward identities and their solution, Nucl. Phys. B 711 (2005) 409 [hep-th/0407060] [INSPIRE].
G. Arutyunov and S. Frolov, On the correspondence between gravity fields and CFT operators, JHEP 04 (2000) 017 [hep-th/0003038] [INSPIRE].
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].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
G.E. Arutyunov and S.A. Frolov, Quadratic action for Type IIB supergravity on AdS 5 × S 5, JHEP 08 (1999) 024 [hep-th/9811106] [INSPIRE].
G. Arutyunov and S. Frolov, Some cubic couplings in type IIB supergravity on AdS 5 × S 5 and three point functions in SYM(4) at large N , Phys. Rev. D 61 (2000) 064009 [hep-th/9907085] [INSPIRE].
G. Arutyunov and S. Frolov, Scalar quartic couplings in type IIB supergravity on AdS 5 × S 5, Nucl. Phys. B 579 (2000) 117 [hep-th/9912210] [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].
D. Chicherin, J. Drummond, P. Heslop and E. Sokatchev, All three-loop four-point correlators of half-BPS operators in planar \( \mathcal{N}=4 \) SYM, JHEP 08 (2016) 053 [arXiv:1512.02926] [INSPIRE].
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: 1808.06788
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
Arutyunov, G., Klabbers, R. & Savin, S. Four-point functions of 1/2-BPS operators of any weights in the supergravity approximation. J. High Energ. Phys. 2018, 118 (2018). https://doi.org/10.1007/JHEP09(2018)118
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2018)118