Four-point functions of 1/2-BPS operators of any weights in the supergravity approximation. (English) Zbl 1398.83119

Summary: 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.


83E50 Supergravity
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81T13 Yang-Mills and other gauge theories in quantum field theory
Full Text: DOI arXiv


[1] L. Rastelli and X. Zhou, Mellin amplitudes for AdS_{5} × \(S\)5, Phys. Rev. Lett.118 (2017) 091602 [arXiv:1608.06624] [INSPIRE].
[2] Rastelli, L.; Zhou, X., How to succeed at holographic correlators without really trying, JHEP, 04, 014, (2018) · Zbl 1390.83420
[3] 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]. · Zbl 1214.81270
[4] D’Hoker, E.; etal., Graviton exchange and complete four point functions in the AdS/CFT correspondence, Nucl. Phys., B 562, 353, (1999) · Zbl 0958.81147
[5] 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].
[6] Arutyunov, G.; Dolan, FA; Osborn, H.; Sokatchev, E., Correlation functions and massive Kaluza-Klein modes in the AdS/CFT correspondence, Nucl. Phys., B 665, 273, (2003) · Zbl 1059.81567
[7] 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]. · Zbl 1059.81568
[8] Berdichevsky, L.; Naaijkens, P., Four-point functions of different-weight operators in the AdS/CFT correspondence, JHEP, 01, 071, (2008)
[9] Uruchurtu, LI, Four-point correlators with higher weight superconformal primaries in the AdS/CFT Correspondence, JHEP, 03, 133, (2009)
[10] L.I. Uruchurtu, Next-next-to-extremal four point functions of N = 4 1\(/\)2 BPS operators in the AdS/CFT correspondence, JHEP08 (2011) 133 [arXiv:1106.0630] [INSPIRE]. · Zbl 1298.81335
[11] G. Arutyunov, S. Frolov, R. Klabbers and S. Savin, Towards 4-point correlation functions of any\( \frac{1}{2} \)-BPS operators from supergravity, JHEP04 (2017) 005 [arXiv:1701.00998] [INSPIRE]. · Zbl 1378.83090
[12] Arutyunov, G.; Klabbers, R.; Savin, S., Four-point functions of all-different-weight chiral primary operators in the supergravity approximation, JHEP, 09, 023, (2018) · Zbl 1398.83118
[13] 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].
[14] Aprile, F.; Drummond, JM; Heslop, P.; Paul, H., Unmixing supergravity, JHEP, 02, 133, (2018) · Zbl 1387.83093
[15] Aprile, F.; Drummond, JM; Heslop, P.; Paul, H., Loop corrections for Kaluza-Klein AdS amplitudes, JHEP, 05, 056, (2018) · Zbl 1391.83099
[16] F. Aprile, J. Drummond, P. Heslop and H. Paul, The double-trace spectrum of N = 4 SYM at strong coupling, arXiv:1802.06889 [INSPIRE].
[17] Dolan, F. A.; Osborn, H., Conformal partial waves and the operator product expansion, Nuclear Physics B, 678, 491-507, (2004) · Zbl 1097.81735
[18] Nirschl, M.; Osborn, H., Superconformal Ward identities and their solution, Nuclear Physics B, 711, 409-479, (2005) · Zbl 1109.81350
[19] Arutyunov, G.; Frolov, S., On the correspondence between gravity fields and CFT operators, JHEP, 04, 017, (2000) · Zbl 0959.81062
[20] Maldacena, JM, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys., 38, 1113, (1999) · Zbl 0969.81047
[21] Witten, E., Anti-de Sitter space and holography, Adv. Theor. Math. Phys., 2, 253, (1998) · Zbl 0914.53048
[22] 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]. · Zbl 1355.81126
[23] Arutyunov, GE; Frolov, SA, Quadratic action for Type IIB supergravity on AdS_{5} × S5, JHEP, 08, 024, (1999) · Zbl 0951.83058
[24] G. Arutyunov and S. Frolov, Some cubic couplings in type IIB supergravity on AdS_{5} × \(S\)5and three point functions in SYM(4) at large N , Phys. Rev.D 61 (2000) 064009 [hep-th/9907085] [INSPIRE].
[25] 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]. · Zbl 0992.83085
[26] D’Hoker, Eric; Freedman, Daniel Z.; Rastelli, Leonardo, AdS/CFT four-point functions: How to succeed at z-integrals without really trying, Nuclear Physics B, 562, 395-411, (1999) · Zbl 0958.81143
[27] 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, JHEP08 (2016) 053 [arXiv:1512.02926] [INSPIRE]. · Zbl 1390.81576
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.