Abstract
The quartic effective action for Kaluza-Klein modes that arises upon compactification of type IIB supergravity on the five-sphere S5 is a starting point for computing the four-point correlation functions of arbitrary weight \( \frac{1}{2} \) -BPS operators in \( \mathcal{N} \) = 4 super Yang-Mills theory in the supergravity approximation. The apparent structure of this action is rather involved, in particular it contains quartic terms with four derivatives which cannot be removed by field redefinitions. By exhibiting intricate identities between certain integrals involving spherical harmonics of S5 we show that the net contribution of these four-derivative terms to the effective action vanishes. Our result is in agreement with and provides further support to the recent conjecture on the Mellin space representation of the four-point correlation function of any \( \frac{1}{2} \) -BPS operators in the supergravity approximation.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
G. Mack, D-independent representation of Conformal Field Theories in D dimensions via transformation to auxiliary Dual Resonance Models. Scalar amplitudes, arXiv:0907.2407 [INSPIRE].
J. Penedones, Writing CFT correlation functions as AdS scattering amplitudes, JHEP 03 (2011) 025 [arXiv:1011.1485] [INSPIRE].
A.L. Fitzpatrick, J. Kaplan, J. Penedones, S. Raju and B.C. van Rees, A Natural Language for AdS/CFT Correlators, JHEP 11 (2011) 095 [arXiv:1107.1499] [INSPIRE].
L. Rastelli and X. Zhou, Mellin amplitudes for AdS 5 × S 5, Phys. Rev. Lett. 118 (2017) 091602 [arXiv:1608.06624] [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].
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].
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 S. Frolov, Four point functions of lowest weight chiral primary operators in N = 4 four-dimensional supersymmetric Yang-Mills theory in supergravity approximation, Phys. Rev. D 62 (2000) 064016 [hep-th/0002170] [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 \( \mathcal{N} \) = 4 1/2-BPS Operators in the AdS/CFT Correspondence, JHEP 08 (2011) 133 [arXiv:1106.0630] [INSPIRE].
G. Arutyunov and S. Frolov, On the correspondence between gravity fields and CFT operators, JHEP 04 (2000) 017 [hep-th/0003038] [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: 1701.00998
Correspondent fellow at Steklov Mathematical Institute, Moscow (Gleb Arutyunov, Sergey Frolov).
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, 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 license, and indicate if changes were made.
About this article
Cite this article
Arutyunov, G., Frolov, S., Klabbers, R. et al. Towards 4-point correlation functions of any \( \frac{1}{2} \) -BPS operators from supergravity. J. High Energ. Phys. 2017, 5 (2017). https://doi.org/10.1007/JHEP04(2017)005
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2017)005