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On structure constants with two spinning twist-two operators. (English) Zbl 1415.81072
Summary: I consider three-point functions of one protected and two unprotected twist-two operators with 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.

81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81T60 Supersymmetric field theories in quantum mechanics
81R12 Groups and algebras in quantum theory and relations with integrable systems
LiteRed; FIRE; FIRE5
Full Text: DOI arXiv
[1] B. Basso, S. Komatsu and P. Vieira, Structure constants and integrable bootstrap in planar N = 4 SYM theory,arXiv:1505.06745[INSPIRE].
[2] Beisert, N.; etal., Review of AdS/CFT integrability: an overview, Lett. Math. Phys., 99, 3, (2012) · Zbl 1268.81126
[3] B. Eden and A. Sfondrini, Three-point functions in\( \mathcal{N}=4 \)SYM: the hexagon proposal at three loops, JHEP02 (2016) 165 [arXiv:1510.01242] [INSPIRE]. · Zbl 1388.81517
[4] B. Basso, V. Goncalves, S. Komatsu and P. Vieira, Gluing hexagons at three loops, Nucl. Phys.B 907 (2016) 695 [arXiv:1510.01683] [INSPIRE]. · Zbl 1336.81052
[5] B. Eden and F. Paul, Half-BPS half-BPS twist two at four loops in N = 4 SYM, arXiv:1608.04222 [INSPIRE].
[6] Gonçalves, V., Extracting OPE coefficient of Konishi at four loops, JHEP, 03, 079, (2017) · Zbl 1377.81171
[7] Basso, B.; Goncalves, V.; Komatsu, S., Structure constants at wrapping order, JHEP, 05, 124, (2017) · Zbl 1380.81289
[8] Georgoudis, A.; Goncalves, V.; Pereira, R., Konishi OPE coefficient at the five loop order, JHEP, 11, 184, (2018) · Zbl 1405.81129
[9] B. Eden and A. Sfondrini, Tessellating cushions: four-point functions in\( \mathcal{N}=4 \)SYM, JHEP10 (2017) 098 [arXiv:1611.05436] [INSPIRE]. · Zbl 1383.81290
[10] Fleury, T.; Komatsu, S., Hexagonalization of correlation functions, JHEP, 01, 130, (2017) · Zbl 1373.81323
[11] Fleury, T.; Komatsu, S., Hexagonalization of correlation functions II: two-particle contributions, JHEP, 02, 177, (2018) · Zbl 1387.81349
[12] B. Basso et al., Asymptotic four point functions, arXiv:1701.04462 [INSPIRE].
[13] 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, JHEP11 (2018) 069 [arXiv:1809.00551] [INSPIRE]. · Zbl 1404.81252
[14] F. Coronado, Perturbative four-point functions in planar\( \mathcal{N}=4 \)SYM from hexagonalization, JHEP01 (2019) 056 [arXiv:1811.00467] [INSPIRE]. · Zbl 1409.81142
[15] T. Bargheer et al., Handling handles: nonplanar integrability in = 4 supersymmetric Yang-Mills theory, Phys. Rev. Lett.121 (2018) 231602 [arXiv:1711.05326] [INSPIRE].
[16] Eden, B.; Jiang, Y.; Plat, D.; Sfondrini, A., Colour-dressed hexagon tessellations for correlation functions and non-planar corrections, JHEP, 02, 170, (2018) · Zbl 1387.81348
[17] T. Bargheer et al., Handling handles. Part II. Stratification and data analysis, JHEP11 (2018) 095 [arXiv:1809.09145] [INSPIRE]. · Zbl 1404.81216
[18] J. Plefka and K. Wiegandt, Three-point functions of twist-two operators in N = 4 SYM at one loop, JHEP10 (2012) 177 [arXiv:1207.4784] [INSPIRE]. · Zbl 1397.81395
[19] Bianchi, MS, A note on three-point functions of unprotected operators, JHEP, 03, 154, (2019) · Zbl 1414.81193
[20] N. Drukker and J. Plefka, The Structure of n-point functions of chiral primary operators in N = 4 super Yang-Mills at one-loop, JHEP04(2009) 001 [arXiv:0812.3341] [INSPIRE].
[21] 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].
[22] 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].
[23] Staudacher, M., The factorized S-matrix of CFT/AdS, JHEP, 05, 054, (2005)
[24] B. Eden and M. Staudacher, Integrability and transcendentality, J. Stat. Mech.0611 (2006) P11014 [hep-th/0603157] [INSPIRE].
[25] 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].
[26] N. Beisert, B. Eden and M. Staudacher, Transcendentality and crossing, J. Stat. Mech.0701 (2007) P01021 [hep-th/0610251] [INSPIRE].
[27] 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].
[28] A.V. Belitsky et al., Anomalous dimensions of leading twist conformal operators, Phys. Rev.D 77 (2008) 045029 [arXiv:0707.2936] [INSPIRE].
[29] Sotkov, GM; Zaikov, RP, Conformal invariant two point and three point functions for fields with arbitrary spin, Rept. Math. Phys., 12, 375, (1977)
[30] 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].
[31] Tkachov, FV, A theorem on analytical calculability of four loop renormalization group functions, Phys. Lett., 100B, 65, (1981)
[32] A.V. Smirnov, Algorithm FIREFeynman Integral REduction, JHEP10 (2008) 107 [arXiv:0807.3243] [INSPIRE].
[33] Smirnov, AV; Smirnov, VA, FIRE4, LiteRed and accompanying tools to solve integration by parts relations, Comput. Phys. Commun., 184, 2820, (2013) · Zbl 1344.81031
[34] Smirnov, AV, FIRE5: a C++ implementation of Feynman Integral REduction, Comput. Phys. Commun., 189, 182, (2015) · Zbl 1344.81030
[35] R.N. Lee, Presenting LiteRed: a tool for the Loop InTEgrals REDuction, arXiv:1212.2685 [INSPIRE].
[36] 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].
[37] S. Laporta and E. Remiddi, The Analytical value of the electron (\(g\) − 2) at order α3in QED, Phys. Lett.B 379 (1996) 283 [hep-ph/9602417] [INSPIRE].
[38] S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations, Int. J. Mod. Phys.A 15 (2000) 5087 [hep-ph/0102033] [INSPIRE]. · Zbl 0973.81082
[39] B. Eden, Three-loop universal structure constants in N = 4 SUSY Yang-Mills theory, arXiv:1207.3112 [INSPIRE].
[40] 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].
[41] D.A. Kosower, Direct solution of integration-by-parts systems, Phys. Rev.D 98 (2018) 025008 [arXiv:1804.00131] [INSPIRE].
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