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ABJM quantum spectral curve and Mellin transform

  • R. N. Lee
  • A. I. OnishchenkoEmail author
Open Access
Regular Article - Theoretical Physics

Abstract

The present techniques for the perturbative solution of quantum spectral curve problems in \( \mathcal{N}=4 \) SYM and ABJM models are limited to the situation when the states quantum numbers are given explicitly as some integer numbers. These techniques are sufficient to recover full analytical structure of the conserved charges provided that we know a finite basis of functions in terms of which they could be written explicitly. It is known that in the case of \( \mathcal{N}=4 \) SYM both the contributions of asymptotic Bethe ansatz and wrapping or finite size corrections are expressed in terms of the harmonic sums. However, in the case of ABJM model only the asymptotic contribution can still be written in the harmonic sums basis, while the wrapping corrections part can not. Moreover, the generalization of harmonic sums basis for this problem is not known. In this paper we present a Mellin space technique for the solution of multiloop Baxter equations, which is the main ingredient for the solution of corresponding quantum spectral problems, and provide explicit results for the solution of ABJM quantum spectral curve in the case of twist 1 operators in sl(2) sector for arbitrary spin values up to four loop order with explicit account for wrapping corrections. It is shown that the result for anomalous dimensions could be expressed in terms of harmonic sums decorated by the fourth root of unity factors, so that maximum transcendentality principle holds.

Keywords

AdS-CFT Correspondence Chern-Simons Theories Integrable Field Theories Supersymmetric Gauge Theory 

Notes

Open Access

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References

  1. [1]
    G. ’t Hooft, A planar diagram theory for strong interactions, Nucl. Phys. B 72 (1974) 461 [INSPIRE].
  2. [2]
    J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  3. [3]
    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].ADSCrossRefGoogle Scholar
  4. [4]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  5. [5]
    N. Beisert et al., Review of AdS/CFT integrability: an overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  6. [6]
    D. Bombardelli et al., An integrability primer for the gauge-gravity correspondence: an introduction, J. Phys. A 49 (2016) 320301 [arXiv:1606.02945] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  7. [7]
    S.J. van Tongeren, Integrability of the AdS 5 × S 5 superstring and its deformations, J. Phys. A 47 (2014) 433001 [arXiv:1310.4854] [INSPIRE].
  8. [8]
    M. de Leeuw, A.C. Ipsen, C. Kristjansen and M. Wilhelm, Introduction to integrability and one-point functions in \( \mathcal{N}=4 \) SYM and its defect cousin, in Les Houches Summer School: Integrability: From Statistical Systems to Gauge Theory, June 6-July, Les Houches, France (2017), arXiv:1708.02525 [INSPIRE].
  9. [9]
    N. Gromov, Introduction to the spectrum of N = 4 SYM and the quantum spectral curve, arXiv:1708.03648 [INSPIRE].
  10. [10]
    S. Komatsu, Lectures on three-point functions in N = 4 supersymmetric Yang-Mills theory, arXiv:1710.03853 [INSPIRE].
  11. [11]
    O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M 2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  12. [12]
    M. Staudacher, The factorized S-matrix of CFT/AdS, JHEP 05 (2005) 054 [hep-th/0412188] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  13. [13]
    G. Arutyunov, S. Frolov and M. Staudacher, Bethe ansatz for quantum strings, JHEP 10 (2004) 016 [hep-th/0406256] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  14. [14]
    N. Beisert, The SU(2|2) dynamic S-matrix, Adv. Theor. Math. Phys. 12 (2008) 945 [hep-th/0511082] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  15. [15]
    N. Beisert, The analytic Bethe ansatz for a chain with centrally extended su(2|2) Symmetry, J. Stat. Mech. 01 (2007) P01017 [nlin/0610017].MathSciNetGoogle Scholar
  16. [16]
    N. Beisert, B. Eden and M. Staudacher, Transcendentality and crossing, J. Stat. Mech. 0701 (2007) P01021 [hep-th/0610251] [INSPIRE].
  17. [17]
    R.A. Janik, The AdS 5 × S 5 superstring worldsheet S-matrix and crossing symmetry, Phys. Rev. D 73 (2006) 086006 [hep-th/0603038] [INSPIRE].
  18. [18]
    G. Arutyunov and S. Frolov, On AdS 5 × S 5 string S-matrix, Phys. Lett. B 639 (2006) 378 [hep-th/0604043] [INSPIRE].
  19. [19]
    G. Arutyunov, S. Frolov and M. Zamaklar, The Zamolodchikov-Faddeev algebra for AdS 5 × S 5 superstring, JHEP 04 (2007) 002 [hep-th/0612229] [INSPIRE].
  20. [20]
    C. Ahn and R.I. Nepomechie, N = 6 super Chern-Simons theory S-matrix and all-loop Bethe ansatz equations, JHEP 09 (2008) 010 [arXiv:0807.1924] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  21. [21]
    J.A. Minahan and K. Zarembo, The Bethe ansatz for N = 4 super-Yang-Mills, JHEP 03 (2003) 013 [hep-th/0212208] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  22. [22]
    N. Beisert and M. Staudacher, The N = 4 SYM integrable super spin chain, Nucl. Phys. B 670 (2003) 439 [hep-th/0307042] [INSPIRE].
  23. [23]
    N. Beisert and M. Staudacher, Long-range P SU (2, 2|4) Bethe Ansatze for gauge theory and strings, Nucl. Phys. B 727 (2005) 1 [hep-th/0504190] [INSPIRE].
  24. [24]
    J.A. Minahan and K. Zarembo, The Bethe ansatz for superconformal Chern-Simons, JHEP 09 (2008) 040 [arXiv:0806.3951] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  25. [25]
    D. Gaiotto, S. Giombi and X. Yin, Spin chains in N = 6 superconformal Chern-Simons-matter theory, JHEP 04 (2009) 066 [arXiv:0806.4589] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  26. [26]
    N. Gromov and P. Vieira, The all loop AdS 4 /CFT 3 Bethe ansatz, JHEP 01 (2009) 016 [arXiv:0807.0777] [INSPIRE].
  27. [27]
    N. Gromov, V. Kazakov and P. Vieira, Exact spectrum of anomalous dimensions of planar N = 4 supersymmetric Yang-Mills theory,Phys. Rev. Lett. 103(2009) 131601 [arXiv:0901.3753] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  28. [28]
    D. Bombardelli, D. Fioravanti and R. Tateo, Thermodynamic Bethe Ansatz for planar AdS/CFT: a proposal, J. Phys. A 42 (2009) 375401 [arXiv:0902.3930] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  29. [29]
    N. Gromov, V. Kazakov, A. Kozak and P. Vieira, Exact spectrum of anomalous dimensions of planar N = 4 supersymmetric Yang-Mills theory: TBA and excited states, Lett. Math. Phys. 91 (2010) 265 [arXiv:0902.4458] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  30. [30]
    G. Arutyunov and S. Frolov, Thermodynamic Bethe ansatz for the AdS 5 × S 5 mirror model, JHEP 05 (2009) 068 [arXiv:0903.0141] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    A. Cavaglia, D. Fioravanti and R. Tateo, Extended Y-system for the AdS 5 /CF T 4 correspondence, Nucl. Phys. B 843 (2011) 302 [arXiv:1005.3016] [INSPIRE].
  32. [32]
    J. Balog and A. Hegedus, AdS 5 × S 5 mirror TBA equations from Y-system and discontinuity relations, JHEP 08 (2011) 095 [arXiv:1104.4054] [INSPIRE].
  33. [33]
    N. Gromov, V. Kazakov, S. Leurent and Z. Tsuboi, Wronskian solution for AdS/CFT Y-system, JHEP 01 (2011) 155 [arXiv:1010.2720] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  34. [34]
    N. Gromov, V. Kazakov, S. Leurent and D. Volin, Solving the AdS/CFT Y-system, JHEP 07 (2012) 023 [arXiv:1110.0562] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  35. [35]
    D. Bombardelli, D. Fioravanti and R. Tateo, TBA and Y-system for planar AdS 4 /CF T 3, Nucl. Phys. B 834 (2010) 543 [arXiv:0912.4715] [INSPIRE].
  36. [36]
    N. Gromov and F. Levkovich-Maslyuk, Y-system, TBA and quasi-classical strings in AdS 4 × CP 3, JHEP 06 (2010) 088 [arXiv:0912.4911] [INSPIRE].
  37. [37]
    A. Cavaglia, D. Fioravanti and R. Tateo, Discontinuity relations for the AdS 4 /CF T 3 correspondence, Nucl. Phys. B 877 (2013) 852 [arXiv:1307.7587] [INSPIRE].
  38. [38]
    D. Correa, J. Maldacena and A. Sever, The quark anti-quark potential and the cusp anomalous dimension from a TBA equation, JHEP 08 (2012) 134 [arXiv:1203.1913] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    N. Drukker, Integrable Wilson loops, JHEP 10 (2013) 135 [arXiv:1203.1617] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  40. [40]
    N. Gromov and F. Levkovich-Maslyuk, Quantum spectral curve for a cusped Wilson line in \( \mathcal{N}=4 \) SYM, JHEP 04 (2016) 134 [arXiv:1510.02098] [INSPIRE].
  41. [41]
    N. Gromov and F. Levkovich-Maslyuk, Quark-anti-quark potential in \( \mathcal{N}=4 \) SYM, JHEP 12 (2016) 122 [arXiv:1601.05679] [INSPIRE].
  42. [42]
    L.F. Alday, D. Gaiotto and J. Maldacena, Thermodynamic bubble ansatz, JHEP 09 (2011) 032 [arXiv:0911.4708] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  43. [43]
    L.F. Alday, J. Maldacena, A. Sever and P. Vieira, Y-system for scattering amplitudes, J. Phys. A 43 (2010) 485401 [arXiv:1002.2459] [INSPIRE].
  44. [44]
    L.F. Alday et al., An operator product expansion for polygonal null Wilson loops, JHEP 04 (2011) 088 [arXiv:1006.2788] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  45. [45]
    B. Basso, A. Sever and P. Vieira, Spacetime and flux tube S-matrices at finite coupling for N = 4 supersymmetric Yang-Mills theory, Phys. Rev. Lett. 111 (2013) 091602 [arXiv:1303.1396] [INSPIRE].
  46. [46]
    B. Basso, J. Caetano, L. Cordova, A. Sever and P. Vieira, OPE for all helicity amplitudes, JHEP 08 (2015) 018 [arXiv:1412.1132] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  47. [47]
    D. Fioravanti, S. Piscaglia and M. Rossi, Asymptotic Bethe Ansatz on the GKP vacuum as a defect spin chain: scattering, particles and minimal area Wilson loops, Nucl. Phys. B 898 (2015) 301 [arXiv:1503.08795] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  48. [48]
    B. Basso, S. Caron-Huot and A. Sever, Adjoint BFKL at finite coupling: a short-cut from the collinear limit, JHEP 01 (2015) 027 [arXiv:1407.3766] [INSPIRE].ADSCrossRefGoogle Scholar
  49. [49]
    M. Alfimov, N. Gromov and V. Kazakov, QCD Pomeron from AdS/CFT quantum spectral curve, JHEP 07 (2015) 164 [arXiv:1408.2530] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  50. [50]
    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].
  51. [51]
    B. Basso, S. Komatsu and P. Vieira, Structure constants and integrable bootstrap in planar N = 4 SYM theory,arXiv:1505.06745[INSPIRE].
  52. [52]
    B. Basso, V. Goncalves and S. Komatsu, Structure constants at wrapping order, JHEP 05 (2017) 124 [arXiv:1702.02154] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  53. [53]
    Y. Jiang, S. Komatsu, I. Kostov and D. Serban, Clustering and the three-point function, J. Phys. A 49 (2016) 454003 [arXiv:1604.03575] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  54. [54]
    I. Balitsky, V. Kazakov and E. Sobko, Structure constant of twist-2 light-ray operators in the Regge limit, Phys. Rev. D 93 (2016) 061701 [arXiv:1506.02038] [INSPIRE].
  55. [55]
    M. de Leeuw, C. Kristjansen and K. Zarembo, One-point functions in defect CFT and integrability, JHEP 08 (2015) 098 [arXiv:1506.06958] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  56. [56]
    I. Buhl-Mortensen, M. de Leeuw, C. Kristjansen and K. Zarembo, One-point functions in AdS/dCFT from matrix product states, JHEP 02 (2016) 052 [arXiv:1512.02532] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  57. [57]
    I. Buhl-Mortensen et al., One-loop one-point functions in gauge-gravity dualities with defects, Phys. Rev. Lett. 117 (2016) 231603 [arXiv:1606.01886] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  58. [58]
    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].
  59. [59]
    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].ADSCrossRefGoogle Scholar
  60. [60]
    V. Kazakov, S. Leurent and D. Volin, T-system on T-hook: grassmannian solution and twisted quantum spectral curve, JHEP 12 (2016) 044 [arXiv:1510.02100] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  61. [61]
    C. Marboe and D. Volin, The full spectrum of AdS 5 /CFT 4 I: representation theory and one-loop Q-system, J. Phys. A 51 (2018) 165401 [arXiv:1701.03704] [INSPIRE].
  62. [62]
    A. Cavagli, D. Fioravanti, N. Gromov and R. Tateo, Quantum spectral curve of the \( \mathcal{N}=6 \) supersymmetric Chern-Simons theory, Phys. Rev. Lett. 113 (2014) 021601 [arXiv:1403.1859] [INSPIRE].
  63. [63]
    D. Bombardelliet al., The full quantum spectral curve for AdS 4 /CF T 3, JHEP 09 (2017) 140 [arXiv:1701.00473] [INSPIRE].
  64. [64]
    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].ADSMathSciNetCrossRefGoogle Scholar
  65. [65]
    L. Anselmetti et al., 12 loops and triple wrapping in ABJM theory from integrability, JHEP 10 (2015) 117 [arXiv:1506.09089] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  66. [66]
    L.N. Lipatov, Next-to-leading corrections to the BFKL equation and the effective action for high energy processes in QCD, Nucl. Phys. Proc. Suppl. 99A (2001) 175 [INSPIRE].ADSCrossRefGoogle Scholar
  67. [67]
    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].ADSCrossRefGoogle Scholar
  68. [68]
    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].ADSMathSciNetCrossRefGoogle Scholar
  69. [69]
    A.V. Kotikov and L.N. Lipatov, DGLAP and BFKL evolution equations in the N = 4 supersymmetric gauge theory, talk given at the 35th Annual Winter School on Nuclear and Particle Physics, February 19-25, Repino, Russia (2001), hep-ph/0112346 [INSPIRE].
  70. [70]
    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].
  71. [71]
    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].ADSMathSciNetCrossRefGoogle Scholar
  72. [72]
    A.V. Kotikov et al., Dressing and wrapping, J. Stat. Mech. 0710 (2007) P10003 [arXiv:0704.3586] [INSPIRE].
  73. [73]
    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].ADSMathSciNetCrossRefGoogle Scholar
  74. [74]
    V.N. Velizhanin, Six-loop anomalous dimension of twist-three operators in N = 4 SYM, JHEP 11 (2010) 129 [arXiv:1003.4717] [INSPIRE].
  75. [75]
    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].
  76. [76]
    C. Marboe and V. Velizhanin, Twist-2 at seven loops in planar \( \mathcal{N}=4 \) SYM theory: full result and analytic properties, JHEP 11 (2016) 013 [arXiv:1607.06047] [INSPIRE].
  77. [77]
    M. Beccaria and G. Macorini, QCD properties of twist operators in the N = 6 Chern-Simons theory, JHEP 06 (2009) 008 [arXiv:0904.2463] [INSPIRE].
  78. [78]
    J.A. Minahan, O. Ohlsson Sax and C. Sieg, Magnon dispersion to four loops in the ABJM and ABJ models, J. Phys. A 43 (2010) 275402 [arXiv:0908.2463] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  79. [79]
    J.A. Minahan, O. Ohlsson Sax and C. Sieg, Anomalous dimensions at four loops in N = 6 superconformal Chern-Simons theories, Nucl. Phys. B 846 (2011) 542 [arXiv:0912.3460] [INSPIRE].
  80. [80]
    G. Papathanasiou and M. Spradlin, Two-loop spectroscopy of short ABJM operators, JHEP 02 (2010) 072 [arXiv:0911.2220] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  81. [81]
    M. Leoni et al., Superspace calculation of the four-loop spectrum in N = 6 supersymmetric Chern-Simons theories, JHEP 12 (2010) 074 [arXiv:1010.1756] [INSPIRE].
  82. [82]
    M. Beccaria, F. Levkovich-Maslyuk and G. Macorini, On wrapping corrections to GKP-like operators, JHEP 03 (2011) 001 [arXiv:1012.2054] [INSPIRE].ADSCrossRefGoogle Scholar
  83. [83]
    M.A. Bandres, A.E. Lipstein and J.H. Schwarz, Studies of the ABJM theory in a formulation with manifest SU(4) R-symmetry, JHEP 09 (2008) 027 [arXiv:0807.0880] [INSPIRE].
  84. [84]
    T. Klose, Review of AdS/CFT integrability, Chapter IV.3: N = 6 Chern-Simons and strings on AdS 4 × CP 3, Lett. Math. Phys. 99 (2012) 401 [arXiv:1012.3999] [INSPIRE].
  85. [85]
    G. Grignani, T. Harmark and M. Orselli, The SU(2) × SU(2) sector in the string dual of N = 6 superconformal Chern-Simons theory, Nucl. Phys. B 810 (2009) 115 [arXiv:0806.4959] [INSPIRE].
  86. [86]
    N. Gromov and G. Sizov, Exact slope and interpolating functions in n = 6 supersymmetric Chern-Simons theory, Phys. Rev. Lett. 113 (2014) 121601 [arXiv:1403.1894] [INSPIRE].
  87. [87]
    A. Cavaglià, N. Gromov and F. Levkovich-Maslyuk, On the exact interpolating function in ABJ theory, JHEP 12 (2016) 086 [arXiv:1605.04888] [INSPIRE].ADSCrossRefGoogle Scholar
  88. [88]
    J. Ablinger, A computer algebra toolbox for harmonic sums related to particle physics, Ph.D. thesis, Linz University, Linz, Austria (2009), arXiv:1011.1176 [INSPIRE].
  89. [89]
    J. Ablinger, Computer algebra algorithms for special functions in particle physics, Ph.D. thesis, Linz University, Linz, Austria (2012), arXiv:1305.0687 [INSPIRE].
  90. [90]
    J. Ablinger, J. Blümlein and C. Schneider, Analytic and algorithmic aspects of generalized harmonic sums and polylogarithms, J. Math. Phys. 54 (2013) 082301 [arXiv:1302.0378] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  91. [91]
    J. Ablinger, J. Blümlein and C. Schneider, Harmonic sums and polylogarithms generated by cyclotomic polynomials, J. Math. Phys. 52 (2011) 102301 [arXiv:1105.6063] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  92. [92]
    J. Blumlein, Structural relations of harmonic sums and Mellin transforms up to weight w = 5, Comput. Phys. Commun. 180 (2009) 2218 [arXiv:0901.3106] [INSPIRE].
  93. [93]
    E. Remiddi and J.A.M. Vermaseren, Harmonic polylogarithms, Int. J. Mod. Phys. A 15 (2000) 725 [hep-ph/9905237] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  94. [94]
    J.A.M. Vermaseren, Harmonic sums, Mellin transforms and integrals, Int. J. Mod. Phys. A 14 (1999) 2037 [hep-ph/9806280] [INSPIRE].
  95. [95]
    L.N. Lipatov, Asymptotic behavior of multicolor QCD at high energies in connection with exactly solvable spin models, JETP Lett. 59 (1994) 596 [hep-th/9311037] [INSPIRE].ADSGoogle Scholar
  96. [96]
    L.D. Faddeev and G.P. Korchemsky, High-energy QCD as a completely integrable model, Phys. Lett. B 342 (1995) 311 [hep-th/9404173] [INSPIRE].ADSCrossRefGoogle Scholar
  97. [97]
    A.V. Kotikov, A. Rej and S. Zieme, Analytic three-loop solutions for N = 4 SYM twist operators, Nucl. Phys. B 813 (2009) 460 [arXiv:0810.0691] [INSPIRE].
  98. [98]
    M. Beccaria, A.V. Belitsky, A.V. Kotikov and S. Zieme, Analytic solution of the multiloop Baxter equation, Nucl. Phys. B 827 (2010) 565 [arXiv:0908.0520] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  99. [99]
    J. Fleischer, A.V. Kotikov and O.L. Veretin, Analytic two loop results for selfenergy type and vertex type diagrams with one nonzero mass, Nucl. Phys. B 547 (1999) 343 [hep-ph/9808242] [INSPIRE].
  100. [100]
    A.V. Kotikov, The property of maximal transcendentality in the N = 4 supersymmetric Yang-Mills, in Subtleties in quantum field theory: Lev Lipatov Festschrift, D. Diakonov ed., St. Petersburg Nucl. Phys. Inst., Russia (2001), arXiv:1005.5029 [INSPIRE].
  101. [101]
    A.V. Kotikov, The property of maximal transcendentality: calculation of Feynman integrals, Theor. Math. Phys. 190 (2017) 391 [arXiv:1601.00486] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  102. [102]
    S. Moch, P. Uwer and S. Weinzierl, Nested sums, expansion of transcendental functions and multiscale multiloop integrals, J. Math. Phys. 43 (2002) 3363 [hep-ph/0110083] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  103. [103]
    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].ADSCrossRefGoogle Scholar
  104. [104]
    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].
  105. [105]
    A.B. Zamolodchikov, ’Fishnet’ diagrams as a completely integrable system, Phys. Lett. B 97 (1980) 63.Google Scholar
  106. [106]
    D. Chicherin, S. Derkachov and A.P. Isaev, Conformal group: R-matrix and star-triangle relation, JHEP 04 (2013) 020 [arXiv:1206.4150] [INSPIRE].ADSCrossRefGoogle Scholar
  107. [107]
    O. Gurdogan and V. Kazakov, New integrable 4D quantum field theories from strongly deformed planar \( \mathcal{N}=4 \) supersymmetric Yang-Mills theory, Phys. Rev. Lett. 117 (2016) 201602 [arXiv:1512.06704] [INSPIRE].
  108. [108]
    J. Caetano, O. Gurdogan and V. Kazakov, Chiral limit of \( \mathcal{N}=4 \) SYM and ABJM and integrable Feynman graphs, JHEP 03 (2018) 077 [arXiv:1612.05895] [INSPIRE].
  109. [109]
    D. Chicherin et al., Yangian symmetry for bi-scalar loop amplitudes, JHEP 05 (2018) 003 [arXiv:1704.01967] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  110. [110]
    B. Basso and L.J. Dixon, Gluing ladder Feynman diagrams into fishnets, Phys. Rev. Lett. 119 (2017) 071601 [arXiv:1705.03545] [INSPIRE].
  111. [111]
    N. Gromov et al., Integrability of conformal fishnet theory, JHEP 01 (2018) 095 [arXiv:1706.04167] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  112. [112]
    D. Chicherin et al., Yangian symmetry for fishnet Feynman graphs, Phys. Rev. D 96 (2017) 121901 [arXiv:1708.00007] [INSPIRE].

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Budker Institute of Nuclear PhysicsNovosibirskRussia
  2. 2.Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear ResearchDubnaRussia
  3. 3.Moscow Institute of Physics and Technology State UniversityDolgoprudnyRussia
  4. 4.Skobeltsyn Institute of Nuclear PhysicsMoscow State UniversityMoscowRussia

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