Abstract
The anomalous dimension of twist-2 operators of arbitrary spin in planar \( \mathcal{N} \) = 4 SYM theory is found at seven loops by using the quantum spectral curve to compute values at fixed spin, and reconstructing the general result using the LLL-algorithm together with modular arithmetic. The result of the analytic continuation to negative spin is presented, and its relation with the recently computed correction to the BFKL and double-logarithmic equation is discussed.
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C. Marboe, V. Velizhanin and D. Volin, Six-loop anomalous dimension of twist-two operators in planar \( \mathcal{N} \) = 4 SYM theory, JHEP 07 (2015) 084 [arXiv:1412.4762] [INSPIRE].
C. Marboe and D. Volin, Quantum spectral curve as a tool for a perturbative quantum field theory, Nucl. Phys. B 899 (2015) 810 [arXiv:1411.4758] [INSPIRE].
N. Gromov, V. Kazakov, S. Leurent and D. Volin, Quantum spectral curve for planar \( \mathcal{N} \) = 4 Super-Yang-Mills theory, Phys. Rev. Lett. 112 (2014) 011602 [arXiv:1305.1939] [INSPIRE].
A. Lenstra, H. Lenstra and L. Lovász, Factoring polynomials with rational coefficients, Math. Ann. 261 (1982) 515.
M. Albrech, D. Cadé, X. Pujol and D. Stehlé, fplll-4.0, a floating-point LLL implementation, https://github.com/dstehle/fplll.
V.G. Gorshkov, V.N. Gribov, L.N. Lipatov and G.V. Frolov, Double logarithmic asymptotics of quantum electrodynamics, Phys. Lett. 22 (1966) 671 [INSPIRE].
R. Kirschner and L.n. Lipatov, Double Logarithmic Asymptotics and Regge Singularities of Quark Amplitudes with Flavor Exchange, Nucl. Phys. B 213 (1983) 122 [INSPIRE].
V.N. Velizhanin, Double-logs, Gribov-Lipatov reciprocity and wrapping, JHEP 08 (2011) 092 [arXiv:1104.4100] [INSPIRE].
L.N. Lipatov, Reggeization of the vector meson and the vacuum singularity in nonabelian gauge theories, Sov. J. Nucl. Phys. 23 (1976) 338 [INSPIRE].
E.A. Kuraev, L.N. Lipatov and V.S. Fadin, The Pomeranchuk singularity in nonabelian gauge theories, Sov. Phys. JETP 45 (1977) 199 [INSPIRE].
I.I. Balitsky and L.N. Lipatov, The Pomeranchuk singularity in quantum chromodynamics, Sov. J. Nucl. Phys. 28 (1978) 822 [INSPIRE].
V.N. Velizhanin, BFKL Pomeron in the next-to-next-to-leading approximation in the planar N = 4 SYM theory, arXiv:1508.02857 [INSPIRE].
N. Gromov, F. Levkovich-Maslyuk and G. Sizov, Pomeron Eigenvalue at Three Loops in \( \mathcal{N} \) = 4 Supersymmetric Yang-Mills Theory, Phys. Rev. Lett. 115 (2015) 251601 [arXiv:1507.04010] [INSPIRE].
M. Staudacher, The factorized S-matrix of CFT/AdS, JHEP 05 (2005) 054 [hep-th/0412188] [INSPIRE].
N. Beisert and M. Staudacher, Long-range PSU (2, 2|4) Bethe Ansatze for gauge theory and strings, Nucl. Phys. B 727 (2005) 1 [hep-th/0504190] [INSPIRE].
N. Beisert, B. Eden and M. Staudacher, Transcendentality and crossing, J. Stat. Mech. 0701 (2007) P01021 [hep-th/0610251] [INSPIRE].
A.V. Kotikov and L.N. Lipatov, DGLAP and BFKL equations in the N = 4 supersymmetric gauge theory, Nucl. Phys. B 661 (2003) 19 [Erratum ibid. B 685 (2004) 405] [hep-ph/0208220] [INSPIRE].
J.A.M. Vermaseren, Harmonic sums, Mellin transforms and integrals, Int. J. Mod. Phys. A 14 (1999) 2037 [hep-ph/9806280] [INSPIRE].
Yu. L. Dokshitzer, G. Marchesini and G.P. Salam, Revisiting parton evolution and the large-x limit, Phys. Lett. B 634 (2006) 504 [hep-ph/0511302] [INSPIRE].
Yu. L. Dokshitzer and G. Marchesini, N = 4 SUSY Yang-Mills: three loops made simple(r), Phys. Lett. B 646 (2007) 189 [hep-th/0612248] [INSPIRE].
M. Beccaria, Yu. L. Dokshitzer and G. Marchesini, Twist 3 of the sl(2) sector of N = 4 SYM and reciprocity respecting evolution, Phys. Lett. B 652 (2007) 194 [arXiv:0705.2639] [INSPIRE].
B. Basso and G.P. Korchemsky, Anomalous dimensions of high-spin operators beyond the leading order, Nucl. Phys. B 775 (2007) 1 [hep-th/0612247] [INSPIRE].
V.N. Gribov and L.N. Lipatov, Deep inelastic ep scattering in perturbation theory, Sov. J. Nucl. Phys. 15 (1972) 438 [INSPIRE].
N. Gromov, V. Kazakov, S. Leurent and D. Volin, Quantum spectral curve for arbitrary state/operator in AdS 5 /CFT 4, JHEP 09 (2015) 187 [arXiv:1405.4857] [INSPIRE].
N. Gromov, F. Levkovich-Maslyuk, G. Sizov and S. Valatka, Quantum spectral curve at work: from small spin to strong coupling in \( \mathcal{N} \) = 4 SYM, JHEP 07 (2014) 156 [arXiv:1402.0871] [INSPIRE].
M. Alfimov, N. Gromov and V. Kazakov, QCD Pomeron from AdS/CFT quantum spectral curve, JHEP 07 (2015) 164 [arXiv:1408.2530] [INSPIRE].
N. Gromov, F. Levkovich-Maslyuk and G. Sizov, Quantum spectral curve and the numerical solution of the spectral problem in AdS 5 /CFT 4, JHEP 06 (2016) 036 [arXiv:1504.06640] [INSPIRE].
T. Lukowski, A. Rej and V.N. Velizhanin, Five-loop anomalous dimension of twist-two operators, Nucl. Phys. B 831 (2010) 105 [arXiv:0912.1624] [INSPIRE].
E. Remiddi and J.A.M. Vermaseren, Harmonic polylogarithms, Int. J. Mod. Phys. A 15 (2000) 725 [hep-ph/9905237] [INSPIRE].
J.A.M. Vermaseren, New features of FORM, math-ph/0010025 [INSPIRE].
V.S. Fadin and L.N. Lipatov, BFKL Pomeron in the next-to-leading approximation, Phys. Lett. B 429 (1998) 127 [hep-ph/9802290] [INSPIRE].
A.V. Kotikov and L.N. Lipatov, NLO corrections to the BFKL equation in QCD and in supersymmetric gauge theories, Nucl. Phys. B 582 (2000) 19 [hep-ph/0004008] [INSPIRE].
S. Caron-Huot and M. Herranen, High-energy evolution to three loops, arXiv:1604.07417 [INSPIRE].
A.V. Kotikov, L.N. Lipatov, A. Rej, M. Staudacher and V.N. Velizhanin, Dressing and wrapping, J. Stat. Mech. 0710 (2007) P10003 [arXiv:0704.3586] [INSPIRE].
J. Blumlein, D.J. Broadhurst and J.A.M. Vermaseren, The multiple zeta value data mine, Comput. Phys. Commun. 181 (2010) 582 [arXiv:0907.2557] [INSPIRE].
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ArXiv ePrint: 1607.06047
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Marboe, C., Velizhanin, V. Twist-2 at seven loops in planar \( \mathcal{N} \) = 4 SYM theory: full result and analytic properties. J. High Energ. Phys. 2016, 13 (2016). https://doi.org/10.1007/JHEP11(2016)013
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DOI: https://doi.org/10.1007/JHEP11(2016)013