Abstract
I consider three-point functions of one protected and two unprotected twist-two operators ccwith spin in \( \mathcal{N}=4 \) SYM at weak coupling. At one loop I formulate an empiric conjecture for the dependence of the corresponding structure constants on the spins of the operators. Using such an ansatz and some input from explicit perturbative results, I fix completely various infinite sets of one-loop structure constants of these three-point functions. Finally, I determine the two-loop corrections to the structure constants for a few fixed values of the spins of the operators.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
B. Basso, S. Komatsu and P. Vieira, Structure constants and integrable bootstrap in planar N = 4 SYM theory,arXiv:1505.06745[INSPIRE].
N. Beisert et al., Review of AdS/CFT integrability: an overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].
B. Eden and A. Sfondrini, Three-point functions in \( \mathcal{N}=4 \) SYM: the hexagon proposal at three loops, JHEP 02 (2016) 165 [arXiv:1510.01242] [INSPIRE].
B. Basso, V. Goncalves, S. Komatsu and P. Vieira, Gluing hexagons at three loops, Nucl. Phys. B 907 (2016) 695 [arXiv:1510.01683] [INSPIRE].
B. Eden and F. Paul, Half-BPS half-BPS twist two at four loops in N = 4 SYM, arXiv:1608.04222 [INSPIRE].
V. Gonçalves, Extracting OPE coefficient of Konishi at four loops, JHEP 03 (2017) 079 [arXiv:1607.02195] [INSPIRE].
B. Basso, V. Goncalves and S. Komatsu, Structure constants at wrapping order, JHEP 05 (2017) 124 [arXiv:1702.02154] [INSPIRE].
A. Georgoudis, V. Goncalves and R. Pereira, Konishi OPE coefficient at the five loop order, JHEP 11 (2018) 184 [arXiv:1710.06419] [INSPIRE].
B. Eden and A. Sfondrini, Tessellating cushions: four-point functions in \( \mathcal{N}=4 \) SYM, JHEP 10 (2017) 098 [arXiv:1611.05436] [INSPIRE].
T. Fleury and S. Komatsu, Hexagonalization of correlation functions, JHEP 01 (2017) 130 [arXiv:1611.05577] [INSPIRE].
T. Fleury and S. Komatsu, Hexagonalization of correlation functions II: two-particle contributions, JHEP 02 (2018) 177 [arXiv:1711.05327] [INSPIRE].
B. Basso et al., Asymptotic four point functions, arXiv:1701.04462 [INSPIRE].
D. Chicherin, A. Georgoudis, V. Gonçalves and R. Pereira, All five-loop planar four-point functions of half-BPS operators in \( \mathcal{N}=4 \) SYM, JHEP 11 (2018) 069 [arXiv:1809.00551] [INSPIRE].
F. Coronado, Perturbative four-point functions in planar \( \mathcal{N}=4 \) SYM from hexagonalization, JHEP 01 (2019) 056 [arXiv:1811.00467] [INSPIRE].
T. Bargheer et al., Handling handles: nonplanar integrability in \ = 4 supersymmetric Yang-Mills theory, Phys. Rev. Lett. 121 (2018) 231602 [arXiv:1711.05326] [INSPIRE].
B. Eden, Y. Jiang, D. le Plat and A. Sfondrini, Colour-dressed hexagon tessellations for correlation functions and non-planar corrections, JHEP 02 (2018) 170 [arXiv:1710.10212] [INSPIRE].
T. Bargheer et al., Handling handles. Part II. Stratification and data analysis, JHEP 11 (2018) 095 [arXiv:1809.09145] [INSPIRE].
J. Plefka and K. Wiegandt, Three-point functions of twist-two operators in N = 4 SYM at one loop, JHEP 10 (2012) 177 [arXiv:1207.4784] [INSPIRE].
M.S. Bianchi, A note on three-point functions of unprotected operators, JHEP 03 (2019) 154 [arXiv:1809.04376] [INSPIRE].
N. Drukker and J. Plefka, The Structure of n-point functions of chiral primary operators in N = 4 super Yang-Mills at one-loop, JHEP 04(2009) 001 [arXiv:0812.3341] [INSPIRE].
A.V. Kotikov, L.N. Lipatov and V.N. Velizhanin, Anomalous dimensions of Wilson operators in N = 4 SYM theory, Phys. Lett. B 557 (2003) 114 [hep-ph/0301021] [INSPIRE].
A.V. Kotikov, L.N. Lipatov, A.I. Onishchenko and V.N. Velizhanin, Three loop universal anomalous dimension of the Wilson operators in N = 4 SUSY Yang-Mills model, Phys. Lett. B 595 (2004) 521 [Erratum ibid. B 632 (2006) 754] [hep-th/0404092] [INSPIRE].
M. Staudacher, The factorized S-matrix of CFT/AdS, JHEP 05 (2005) 054 [hep-th/0412188] [INSPIRE].
B. Eden and M. Staudacher, Integrability and transcendentality, J. Stat. Mech. 0611 (2006) P11014 [hep-th/0603157] [INSPIRE].
A.V. Belitsky, G.P. Korchemsky and D. Mueller, Towards Baxter equation in supersymmetric Yang-Mills theories, Nucl. Phys. B 768 (2007) 116 [hep-th/0605291] [INSPIRE].
N. Beisert, B. Eden and M. Staudacher, Transcendentality and crossing, J. Stat. Mech. 0701 (2007) P01021 [hep-th/0610251] [INSPIRE].
V.N. Velizhanin, Three-loop renormalization of the N = 1, N = 2, N = 4 supersymmetric Yang-Mills theories, Nucl. Phys. B 818 (2009) 95 [arXiv:0809.2509] [INSPIRE].
A.V. Belitsky et al., Anomalous dimensions of leading twist conformal operators, Phys. Rev. D 77 (2008) 045029 [arXiv:0707.2936] [INSPIRE].
G.M. Sotkov and R.P. Zaikov, Conformal invariant two point and three point functions for fields with arbitrary spin, Rept. Math. Phys. 12 (1977) 375 [INSPIRE].
K.G. Chetyrkin and F.V. Tkachov, Integration by parts: the algorithm to calculate β-functions in 4 loops, Nucl. Phys. B 192 (1981) 159 [INSPIRE].
F.V. Tkachov, A theorem on analytical calculability of four loop renormalization group functions, Phys. Lett. 100B (1981) 65 [INSPIRE].
A.V. Smirnov, Algorithm FIRE — Feynman Integral REduction, JHEP 10 (2008) 107 [arXiv:0807.3243] [INSPIRE].
A.V. Smirnov and V.A. Smirnov, FIRE4, LiteRed and accompanying tools to solve integration by parts relations, Comput. Phys. Commun. 184 (2013) 2820 [arXiv:1302.5885] [INSPIRE].
A.V. Smirnov, FIRE5: a C++ implementation of Feynman Integral REduction, Comput. Phys. Commun. 189 (2015) 182 [arXiv:1408.2372] [INSPIRE].
R.N. Lee, Presenting LiteRed: a tool for the Loop InTEgrals REDuction, arXiv:1212.2685 [INSPIRE].
R.N. Lee, LiteRed 1.4: a powerful tool for reduction of multiloop integrals, J. Phys. Conf. Ser. 523 (2014) 012059 [arXiv:1310.1145] [INSPIRE].
S. Laporta and E. Remiddi, The Analytical value of the electron (g − 2) at order α 3 in QED, Phys. Lett. B 379 (1996) 283 [hep-ph/9602417] [INSPIRE].
S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations, Int. J. Mod. Phys. A 15 (2000) 5087 [hep-ph/0102033] [INSPIRE].
B. Eden, Three-loop universal structure constants in N = 4 SUSY Yang-Mills theory, arXiv:1207.3112 [INSPIRE].
F.A. Dolan and H. Osborn, Conformal partial wave expansions for N = 4 chiral four point functions, Annals Phys. 321 (2006) 581 [hep-th/0412335] [INSPIRE].
D.A. Kosower, Direct solution of integration-by-parts systems, Phys. Rev. D 98 (2018) 025008 [arXiv:1804.00131] [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: 1901.00679
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
Bianchi, M.S. On structure constants with two spinning twist-two operators. J. High Energ. Phys. 2019, 59 (2019). https://doi.org/10.1007/JHEP04(2019)059
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2019)059