Toward an analytic perturbative solution for the ABJM quantum spectral curve

R. N. Lee ; A. I. Onischenko

Teoretičeskaâ i matematičeskaâ fizika, Tome 198 (2019) no. 2, pp. 292-308

Résumé

We recently showed how nonhomogeneous second-order difference equations that appear in describing the ABJM quantum spectral curve can be solved using a Mellin space technique. In particular, we provided explicit results for anomalous dimensions of twist-$1$ operators in the $sl(2)$ sector at arbitrary spin values up to the four-loop order. We showed that the obtained results can be expressed in terms of harmonic sums with additional factors in the form of a fourth root of unity, and the maximum transcendentality principle therefore holds. Here, we show that the same result can also be obtained by directly solving the mentioned difference equations in the space of the spectral parameter $u$. The solution involves new highly nontrivial identities between hypergeometric functions, which can have various applications. We expect that this method can be generalized both to higher loop orders and to other theories, such as the $\mathcal N=4$ supersymmetric Yang–Mills theory.

Détail

Keywords: quantum spectral curve, ABJM model, Baxter equation.
Mots-clés : spin chain, anomalous dimension

Bibliographie

[1] G. 't Hooft, “A planar diagram theory for strong interactions”, Nucl. Phys. B, 72:3 (1974), 461–473 | DOI

[2] J. M. Maldacena, “The large $N$ limit of superconformal field theories and supergravity”, Internat. J. Theor. Phys., 38:4 (1999), 1113–1133, arXiv: ; “The large $N$ limit of superconformal field theories and supergravity”, Adv. Theor. Math. Phys., 2:2 (1998), 231–252 hep-th/9711200 | DOI | MR | DOI | MR | Zbl

[3] S. S. Gubser, I. R. Klebanov, A. M. Polyakov, “Gauge theory correlators from non-critical string theory”, Phys. Lett. B, 428:1–2 (1998), 105–114, arXiv: hep-th/9802109 | DOI | MR

[4] E. Witten, “Anti-de Sitter space and holography”, Adv. Theor. Math. Phys., 2:2 (1998), 253–291, arXiv: hep-th/9802150 | DOI | MR

[5] N. Beisert, C. Ahn, L. F. Alday et al., “Review of AdS/CFT integrability: an overview”, Lett. Math. Phys., 99:1–3 (2012), 3–32, arXiv: 1012.3982 | DOI | MR

[6] D. Bombardelli, A. Cagnazzo, R. Frassek, F. Levkovich-Maslyuk, F. Loebbert, S. Negro, I. M. Szécsényi, A. Sfondrini, S. J. van Tongeren, A. Torrielli, “An integrability primer for the gauge-gravity correspondence: an introduction”, J. Phys. A: Math. Theor., 49:32 (2016), 320301, 10 pp., arXiv: 1606.02945 | DOI | MR

[7] S. J. van Tongeren, “Integrability of the ${\rm AdS}_{5}\times {\rm S}^{5}$ superstring and its deformations”, J. Phys. A: Math. Theor., 47:43 (2014), 433001, 213 pp., arXiv: 1310.4854 | DOI | MR

[8] M. de Leeuw, A. C. Ipsen, C. Kristjansen, M. Wilhelm, “Introduction to integrability and one-point functions in $\mathcal N=4$ SYM and its defect cousin”, Integrability: From Statistical Systems to Gauge Theory (Les Houches, France, 6 June – 1 July, 2016), Les Houches School of Physics, Les Houches, France, 2017, arXiv: 1708.02525

[9] N. Gromov, Introduction to the spectrum of ${\mathcal N=4}$ SYM and the quantum spectral curve, arXiv: 1708.03648

[10] S. Komatsu, Lectures on three-point functions in ${\mathcal N=4}$ supersymmetric Yang–Mills theory, arXiv: 1710.03853

[11] V. Kazakov, “Quantum spectral curve of $\gamma$-twisted ${\mathcal N=4}$ SYM theory and fishnet CFT”, Rev. Math. Phys., 30:7 (2018), 1840010, arXiv: 1802.02160 | DOI | MR

[12] O. Aharony, O. Bergman, D. L. Jafferis, J. Maldacena, “$N=6$ superconformal Chern–Simons-matter theories $M2$-branes and their gravity duals”, JHEP, 10 (2008), 091, 38 pp., arXiv: 0806.1218 | DOI | MR

[13] M. Staudacher, “The factorized $S$-matrix of CFT/AdS”, JHEP, 05 (2005), 054, 35 pp., arXiv: hep-th/0412188 | DOI | MR

[14] G. Arutyunov, S. Frolov, M. Staudacher, “Bethe ansatz for quantum strings”, JHEP, 10 (2004), 016, 21 pp., arXiv: hep-th/0406256 | DOI | MR

[15] N. Beisert, “The $SU(2|2)$ dynamic S-matrix”, Adv. Theor. Math. Phys., 12:5 (2008), 945–979, arXiv: hep-th/0511082 | DOI | MR

[16] N. Beisert, “The analytic Bethe ansatz for a chain with centrally extended $\mathfrak{su}(2|2)$ symmetry”, J. Stat. Mech., 01 (2007), P01017, 63 pp., arXiv: nlin/0610017 | DOI | MR

[17] N. Beisert, B. Eden, M. Staudacher, “Transcendentality and Crossing”, J. Stat. Mech., 2007:01 (2007), P01021, arXiv: hep-th/0610251 | DOI

[18] R. A. Janik, “The $\mathrm{AdS}_5\times S^5$ superstring worldsheet $S$-matrix and crossing symmetry”, Phys. Rev. D, 73:8 (2006), 086006, 10 pp., arXiv: hep-th/0603038 | DOI | MR

[19] G. Arutyunov, S. Frolov, “On $\mathrm{AdS}_5\times S^5$ string S-matrix”, Phys. Lett. B, 639:3–4 (2006), 378–382, arXiv: hep-th/0604043 | DOI | MR

[20] G. Arutyunov, S. Frolov, M. Zamaklar, “The Zamolodchikov–Faddeev algebra for $\mathrm{AdS}_5\times S^5$ superstring”, JHEP, 04 (2007), 002, 38 pp., arXiv: hep-th/0612229 | DOI | MR

[21] C. Ahn, R. I. Nepomechie, “$\mathscr N=6$ super Chern–Simons theory $S$-matrix and allloop Bethe ansatz equations”, JHEP, 09 (2008), 010, 12 pp., arXiv: 0807.1924 | DOI | MR

[22] J. A. Minahan, K. Zarembo, “The Bethe ansatz for $\mathcal N=4$ super Yang–Mills”, JHEP, 03 (2003), 013, 29 pp., arXiv: hep-th/0212208 | DOI | MR

[23] N. Beisert, M. Staudacher, “The $\mathcal N=4$ SYM integrable super spin chain”, Nucl. Phys. B, 670:3 (2003), 439–463, arXiv: hep-th/0307042 | DOI | MR

[24] N. Beisert, M. Staudacher, “Long-range $\mathfrak{psu}(2; 2|4)$ Bethe ansatze for gauge theory and strings”, Nucl. Phys. B, 727:1–2 (2005), 1–62, arXiv: hep-th/0504190 | DOI | MR

[25] J. A. Minahan, K. Zarembo, “The Bethe ansatz for superconformal Chern–Simons”, JHEP, 09 (2008), 040, 22 pp., arXiv: 0806.3951 | DOI | MR

[26] D. Gaiotto, S. Giombi, X. Yin, “Spin chains in $N=6$ superconformal Chern–Simons-matter theory”, JHEP, 04 (2009), 066, 18 pp., arXiv: 0806.4589 | DOI | MR

[27] N. Gromov, P. Vieira, “The all loop $AdS_4/CFT_3$ Bethe ansatz”, JHEP, 01 (2009), 016, 27 pp., arXiv: 0807.0777 | DOI | MR

[28] N. Gromov, V. Kazakov, P. Vieira, “Exact spectrum of anomalous dimensions of planar $\mathscr N=4$ supersymmetric Yang–Mills theory”, Phys. Rev. Lett., 103:13 (2009), 131601, 4 pp., arXiv: 0901.3753 | DOI | MR

[29] D. Bombardelli, D. Fioravanti, R. Tateo, “Thermodynamic Bethe ansatz for planar AdS/CFT: a proposal”, J. Phys. A: Math. Theor., 42:37 (2009), 375401, 20 pp., arXiv: 0902.3930 | MR

[30] N. Gromov, V. Kazakov, A. Kozak, P. Vieira, “Exact spectrum of anomalous dimensions of planar $\mathcal N=4$ supersymmetric Yang–Mills theory: TBA and excited states”, Lett. Math. Phys., 91:3 (2010), 265–287, arXiv: 0902.4458 | DOI | MR

[31] G. Arutyunov, S. Frolov, “Thermodynamic Bethe ansatz for the AdS$_5\times S^5$ mirror model”, JHEP, 05 (2009), 068, 29 pp., arXiv: 0903.0141 | DOI | MR

[32] A. Cavaglia, D. Fioravanti, R. Tateo, “Extended $Y$-system for the $\mathrm{AdS}_5/\mathrm{CFT}_4$ correspondence”, Nucl. Phys. B, 843:1 (2011), 302–343, arXiv: 1005.3016 | DOI | MR

[33] J. Balog, Á. Hegedűs, “$AdS_5\times S^5$ mirror TBA equations from $Y$-system and discontinuity relations”, JHEP, 08 (2011), 095, 68 pp., arXiv: 1104.4054 | DOI | MR

[34] N. Gromov, V. Kazakov, S. Leurent, Z. Tsuboi, “Wronskian solution for AdS/CFT Y-system”, JHEP, 01 (2011), 155, 32 pp., arXiv: 1010.2720 | DOI | MR

[35] N. Gromov, V. Kazakov, S. Leurent, D. Volin, “Solving the AdS/CFT Y-system”, JHEP, 07 (2012), 023, 65 pp., arXiv: 1110.0562 | DOI | MR

[36] D. Bombardelli, D. Fioravanti, R. Tateo, “TBA and Y-system for planar AdS$_4$/CFT$_3$”, Nucl. Phys. B, 834:3 (2010), 543–561, arXiv: 0912.4715 | DOI | MR

[37] N. Gromov, F. Levkovich-Maslyuk, “Y-system, TBA and quasi-classical strings in AdS$_4 \times \mathbb{CP}^3$”, JHEP, 06 (2010), 088, 37 pp., arXiv: 0912.4911 | DOI | MR

[38] A. Cavaglià, D. Fioravanti, R. Tateo, “Discontinuity relations for the AdS$_4$/CFT$_3$ correspondence”, Nucl. Phys. B, 877:3 (2013), 852–884, arXiv: 1307.7587 | DOI | MR

[39] D. Correa, J. Maldacena, A. Sever, “The quark anti-quark potential and the cusp anomalous dimension from a TBA equation”, JHEP, 08 (2012), 134, 56 pp., arXiv: 1203.1913 | DOI

[40] N. Drukker, “Integrable Wilson loops”, JHEP, 10 (2013), 135, 38 pp., arXiv: 1203.1617 | DOI | MR

[41] N. Gromov, F. Levkovich-Maslyuk, “Quantum spectral curve for a cusped Wilson line in $\mathcal N=4$ SYM”, JHEP, 04 (2016), 134, 41 pp., arXiv: 1510.02098 | DOI

[42] N. Gromov, F. Levkovich-Maslyuk, “Quark-anti-quark potential in $\mathcal N=4$ SYM”, JHEP, 12 (2016), 122, 29 pp., arXiv: 1601.05679 | DOI

[43] L. F. Alday, D. Gaiotto, J. Maldacena, “Thermodynamic bubble ansatz”, JHEP, 09 (2011), 032, 46 pp., arXiv: 0911.4708 | DOI | MR

[44] L. F. Alday, J. Maldacena, A. Sever, P. Vieira, “$Y$-system for scattering amplitudes”, J. Phys. A: Math. Theor., 43:48 (2010), 485401, 57 pp., arXiv: 1002.2459 | MR

[45] L. F. Alday, D. Gaiotto, J. Maldacena, A. Sever, P. Vieira, “An operator product expansion for polygonal null Wilson loops”, JHEP, 04 (2011), 088, 41 pp., arXiv: 1006.2788 | DOI | MR

[46] B. Basso, A. Sever, P. Vieira, “Spacetime and flux tube $S$-matrices at finite coupling for $\mathscr N=4$ supersymmetric Yang–Mills theory”, Phys. Rev. Lett., 111:9 (2013), 091602, 4 pp., arXiv: 1303.1396 | DOI

[47] B. Basso, J. Caetano, L. Cordova, A. Sever, P. Vieira, “OPE for all helicity amplitudes”, JHEP, 08 (2015), 018, 28 pp., arXiv: 1412.1132 | DOI | MR

[48] D. Fioravanti, S. Piscaglia, 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), 301–400, arXiv: 1503.08795 | DOI | MR

[49] B. Basso, S. Caron-Huot, A. Sever, “Adjoint BFKL at finite coupling: a shortcut from the collinear limit”, JHEP, 01 (2015), 027, 46 pp., arXiv: 1407.3766 | DOI

[50] M. Alfimov, N. Gromov, V. Kazakov, “QCD pomeron from AdS/CFT quantum spectral curve”, JHEP, 07 (2015), 164, 24 pp., arXiv: 1408.2530 | DOI | MR

[51] N. Gromov, F. Levkovich-Maslyuk, G. Sizov, “Pomeron eigenvalue at three loops in $\mathcal N=4$ supersymmetric Yang–Mills theory”, Phys. Rev. Lett., 115:25 (2015), 251601, 5 pp., arXiv: 1507.04010 | DOI | MR

[52] M. Alfimov, N. Gromov, G. Sizov, “BFKL spectrum of $\mathcal N=4$ SYM: non-zero conformal spin”, JHEP, 07 (2018), 181, 78 pp., arXiv: 1802.06908 | DOI

[53] B. Basso, S. Komatsu, P. Vieira, Structure constants and integrable bootstrap in planar $\mathcal N=4$ SYM theory, arXiv: 1505.06745

[54] B. Basso, V. Gonçalves, S. Komatsu, “Structure constants at wrapping order”, JHEP, 05 (2017), 124, 69 pp., arXiv: 1702.02154 | DOI | MR

[55] Y. Jiang, S. Komatsu, I. Kostov, D. Serban, “Clustering and the three-point function”, J. Phys. A: Math. Theor., 49:45 (2016), 454003, 59 pp., arXiv: 1604.03575 | DOI | MR

[56] I. Balitsky, V. Kazakov, E. Sobko, “Structure constant of twist-2 light-ray operators in the Regge limit”, Phys. Rev. D, 93:6 (2016), 061701, 6 pp., arXiv: 1506.02038 | DOI | MR

[57] A. Cavaglià, N. Gromov, F. Levkovich-Maslyuk, “Quantum spectral curve and structure constants in $\mathcal N=4$ SYM: cusps in the ladder limit”, JHEP, 10 (2018), 060, 68 pp., arXiv: 1802.04237 | DOI

[58] B. Eden, A. Sfondrini, “Tessellating cushions: four-point functions in $\mathcal N=4$ SYM”, JHEP, 10 (2017), 098, 12 pp., arXiv: 1611.05436 | DOI | MR

[59] B. Eden, Y. Jiang, D. le Plat, A. Sfondrini, “Colour-dressed hexagon tessellations for correlation functions and non-planar corrections”, JHEP, 02 (2018), 170, 44 pp., arXiv: 1710.10212 | DOI | MR

[60] T. Bargheer, J. Caetano, T. Fleury, S. Komatsu, P. Vieira, Handling handles I: nonplanar integrability, arXiv: 1711.05326

[61] T. Fleury, S. Komatsu, “Hexagonalization of correlation functions II: two-particle contributions”, JHEP, 02 (2018), 177, 34 pp., arXiv: 1711.05327 | DOI | MR

[62] S. Giombi, S. Komatsu, “Exact correlators on the Wilson loop in $\mathcal N=4$ SYM: localization defect CFT, and integrability”, JHEP, 05 (2018), 109, 45 pp., arXiv: 1802.05201 | DOI | MR

[63] B. Eden, Y. Jiang, M. de Leeuw, T. Meier, D. le Plat, A. Sfondrini, Positivity of hexagon perturbation theory, arXiv: 1806.06051

[64] M. de Leeuw, C. Kristjansen, K. Zarembo, “One-point functions in defect CFT and integrability”, JHEP, 08 (2015), 098, 25 pp., arXiv: 1506.06958 | DOI | MR

[65] I. Buhl-Mortensen, M. de Leeuw, C. Kristjansen, K. Zarembo, “One-point functions in AdS/dCFT from matrix product states”, JHEP, 02 (2016), 052, 21 pp., arXiv: 1512.02532 | DOI | MR

[66] I. Buhl-Mortensen, M. de Leeuw, A. C. Ipsen, C. Kristjansen, M. Wilhelm, “One-loop one-point functions in gauge-gravity dualities with defects”, Phys. Rev. Lett., 117:23 (2016), 231603, 6 pp., arXiv: 1606.01886 | DOI | MR

[67] T. Harmark, M. Wilhelm, “Hagedorn temperature of AdS$_5$/CFT$_4$ via integrability”, Phys. Rev. Lett., 120:7 (2018), 071605, 6 pp., arXiv: 1706.03074 | DOI

[68] T. Harmark, M. Wilhelm, “The Hagedorn temperature of AdS$_5$/CFT$_4$ at finite coupling via the Quantum Spectral Curve”, Phys. Lett. B, 786 (2018), 53–58, arXiv: 1803.04416 | DOI | MR

[69] N. Gromov, V. Kazakov, S. Leurent, D. Volin, “Quantum spectral curve for planar $\mathcal N=4$ Super-Yang–Mills theory”, Phys. Rev. Lett., 112:1 (2014), 011602, 5 pp., arXiv: 1305.1939 | DOI

[70] N. Gromov, V. Kazakov, S. Leurent, D. Volin, “Quantum spectral curve for arbitrary state/operator in AdS$_5$/CFT$_4$”, JHEP, 09 (2015), 187, 104 pp., arXiv: 1405.4857 | DOI | MR

[71] V. Kazakov, S. Leurent, D. Volin, “T-system on T-hook: grassmannian solution and twisted quantum spectral curve”, JHEP, 12 (2016), 044, 118 pp., arXiv: 1510.02100 | DOI | MR

[72] C. Marboe, D. Volin, “The full spectrum of AdS$_5$/CFT$_4$ I: representation theory and one-loop Q-system”, J. Phys. A: Math. Theor., 51:16 (2018), 165401, 46 pp., arXiv: 1701.03704 | MR

[73] A. Cavaglià, D. Fioravanti, N. Gromov, R. Tateo, “Quantum spectral curve of the $\mathcal N=6$ supersymmetric Chern–Simons theory”, Phys. Rev. Lett., 113:2 (2014), 021601, 5 pp., arXiv: 1403.1859 | DOI

[74] D. Bombardelli, A. Cavaglià, D. Fioravanti, N. Gromov, R. Tateo, “The full quantum spectral curve for AdS$_4$/CFT$_3$”, JHEP, 09 (2017), 140, 70 pp., arXiv: 1701.00473 | DOI | MR

[75] R. Klabbers, S. J. van Tongeren, “Quantum Spectral Curve for the eta-deformed AdS5xS5 superstring”, Nucl. Phys. B, 925 (2017), 252–318, arXiv: 1708.02894 | DOI | MR

[76] N. Gromov, F. Levkovich-Maslyuk, G. Sizov, “Quantum spectral curve and the numerical solution of the spectral problem in AdS$_5$/CFT$_4$”, JHEP, 06 (2016), 036, 26 pp., arXiv: 1504.06640 | DOI | MR

[77] Á. Hegedűs, J. Konczer, “Strong coupling results in the AdS$_{5}$/CFT$_{4}$ correspondence from the numerical solution of the quantum spectral curve”, JHEP, 08 (2016), 061, 55 pp., arXiv: 1604.02346 | DOI | MR

[78] D. Bombardelli, A. Cavaglià, R. Conti, R. Tateo, “Exploring the spectrum of planar AdS$_{4}$/CFT$_{3}$ at finite coupling”, JHEP, 04 (2018), 117, 40 pp., arXiv: 1803.04748 | DOI | MR

[79] C. Marboe, D. Volin, “Quantum spectral curve as a tool for a perturbative quantum field theory”, Nucl. Phys. B, 899 (2015), 810–847, arXiv: 1411.4758 | DOI | MR

[80] L. Anselmetti, D. Bombardelli, A. Cavaglià, R. Tateo, “12 loops and triple wrapping in ABJM theory from integrability”, JHEP, 10 (2015), 117, 32 pp., arXiv: 1506.09089 | DOI | MR

[81] R. N. Lee, A. I. Onishchenko, “ABJM quantum spectral curve and Mellin transform”, JHEP, 05 (2018), 179, 28 pp., arXiv: 1712.00412 | DOI | MR

[82] M. A. Bandres, A. E. Lipstein, J. H. Schwarz, “Studies of the ABJM theory in a formulation with manifest SU(4) R-symmetry”, JHEP, 09 (2008), 027, 17 pp., arXiv: 0807.0880 | DOI | MR

[83] T. Klose, “Review of AdS/CFT integrability chapter IV.3: $N=6$ Chern–Simons and STRINGS on AdS$_4 \times \mathbb{CP}_3$”, Lett. Math. Phys., 99:1–3 (2012), 401–423, arXiv: 1012.3999 | DOI | MR

[84] G. Grignani, T. Harmark, M. Orselli, “The $SU(2) \times SU(2)$ sector in the string dual of $\mathscr N=6$ superconformal Chern–Simons theory”, Nucl. Phys. B, 810:1–2 (2009), 115–134, arXiv: 0806.4959 | DOI | MR

[85] A. V. Kotikov, L. N. Lipatov, “DGLAP and BFKL equations in the $N=4$ supersymmetric gauge theory”, Nucl. Phys. B, 661:1–2 (2003), 19–61, arXiv: ; Erratum, 685:1–2 (2004), 405–407 hep-ph/0208220 | DOI | DOI

[86] A. V. Kotikov, L. N. Lipatov, A. I. Onishchenko, V. N. Velizhanin, “Three loop universal anomalous dimension of the Wilson operators in $\mathcal N=4$ SUSY Yang–Mills model”, Phys. Lett. B, 595:1–4 (2004), 521–529, arXiv: ; Erratum, Phys. Lett. B, 632:5–6 (2006), 754–756 hep-th/0404092 | DOI | MR | DOI

[87] M. Beccaria, G. Macorini, “QCD properties of twist operators in the $\mathscr N=6$ Chern–Simons theory”, JHEP, 06 (2009), 008, 21 pp., arXiv: 0904.2463 | DOI | MR

[88] M. Beccaria, F. Levkovich-Maslyuk, G. Macorini, “On wrapping corrections to GKP-like operators”, JHEP, 03 (2011), 001, 37 pp., arXiv: 1012.2054 | DOI

[89] J. Ablinger, J. Blümlein, C. Schneider, “Analytic and algorithmic aspects of generalized harmonic sums and polylogarithms”, J. Math. Phys., 54:8 (2013), 082301, 74 pp., arXiv: 1302.0378 | DOI | MR

[90] J. Ablinger, J. Blümlein, C. Schneider, “Harmonic sums and polylogarithms generated by cyclotomic polynomials”, J. Math. Phys., 52:10 (2011), 102301, 52 pp., arXiv: 1105.6063 | DOI | MR

[91] A. B. Zamolodchikov, “‘Fishing-net’ diagrams as a completely integrable system”, Phys. Lett. B, 97:1 (1980), 63–66 | DOI | MR

[92] D. Chicherin, S. Derkachov, A. P. Isaev, “Conformal group: R-matrix and star-triangle relation”, JHEP, 04 (2013), 020, 49 pp., arXiv: 1206.4150 | DOI | MR

[93] Ö. Gürdoǧan, V. Kazakov, “New integrable 4D quantum field theories from strongly deformed planar $\mathcal N=4$ supersymmetric Yang–Mills theory”, Phys. Rev. Lett., 117:20 (2016), 201602, 6 pp., arXiv: ; Addendum, 117:25, 259903 1512.06704 | DOI

[94] J. Caetano, O. Gürdoǧan, V. Kazakov, Chiral limit of $\mathcal N=4$ SYM and ABJM and integrable Feynman graphs, arXiv: 1612.05895

[95] D. Chicherin, V. Kazakov, F. Loebbert, D. Müller, D.-l. Zhong, “Yangian symmetry for bi-scalar loop amplitudes”, JHEP, 05 (2018), 003, 39 pp., arXiv: 1704.01967 | DOI | MR

[96] B. Basso, L. J. Dixon, “Gluing ladder Feynman diagrams into fishnets”, Phys. Rev. Lett., 119:7 (2017), 071601, 6 pp., arXiv: 1705.03545 | DOI | MR

[97] N. Gromov, V. Kazakov, G. Korchemsky, S. Negro, G. Sizov, “Integrability of conformal fishnet theory”, JHEP, 01 (2018), 095, 75 pp., arXiv: 1706.04167 | DOI | MR

[98] D. Chicherin, V. Kazakov, F. Loebbert, D. Müller, D.-l. Zhong, “Yangian symmetry for fishnet Feynman graphs”, Phys. Rev. D, 96:12 (2017), 121901, 6 pp., arXiv: 1708.00007 | DOI

[99] D. Grabner, N. Gromov, V. Kazakov, G. Korchemsky, “Strongly $\gamma$-deformed $\mathcal N=4$ SYM as an integrable CFT”, Phys. Rev. Lett., 120:11 (2018), 111601, 6 pp., arXiv: 1711.04786 | DOI

[100] V. Kazakov, E. Olivucci, “Bi-scalar integrable CFT at any dimension”, Phys. Rev. Lett., 121:13 (2018), 131601, 6 pp., arXiv: 1801.09844 | DOI