Quantum spectral curve at work: from small spin to strong coupling in N = 4 SYM

Journal of High Energy Physics

Volumn 2014, Issue 7, 2014, Pages

  Gromov, Nikolay ^a,b   Levkovich Maslyuk, Fedor ^a   Sizov, Grigory ^a   Valatka, Saulius ^a  

^a KING'S COLLEGE LONDON   (United Kingdom)

^b St Petersburg INP Gatchina ^*  (Russian Federation)

Author keywords

AdS CFT Correspondence; Integrable Field Theories; Strong Coupling Expansion; Supersymmetric gauge theory

Indexed keywords

EID: 84919948863     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP07(2014)156     Document Type: Article

References (96)

1. N. Beisert et al., Review of AdS/CFT Integrability: An Overview, Lett. Math. Phys.99 (2012) 3 [arXiv:1012.3982] [INSPIRE].
2. 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].
3. C. Sieg and A. Torrielli, Wrapping interactions and the genus expansion of the 2-point function of composite operators, Nucl. Phys.B 723 (2005) 3 [hep-th/0505071] [INSPIRE].
4. J. Ambjorn, R.A. Janik and C. Kristjansen, Wrapping interactions and a new source of corrections to the spin-chain/string duality, Nucl. Phys.B 736 (2006) 288 [hep-th/0510171] [INSPIRE].
5. 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].
6. 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].
7. 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].
8. G. Arutyunov and S. Frolov, Thermodynamic Bethe Ansatz for the AdS5 × S5Mirror Model, JHEP05 (2009) 068 [arXiv:0903.0141] [INSPIRE].
9. A. Cavaglia, D. Fioravanti and R. Tateo, Extended Y-system for the AdS5/CFT4correspondence, Nucl. Phys.B 843 (2011) 302 [arXiv:1005.3016] [INSPIRE].
10. J. Balog and A. Hegedus, Hybrid-NLIE for the AdS/CFT spectral problem, JHEP08 (2012) 022 [arXiv:1202.3244] [INSPIRE].
11. N. Gromov, V. Kazakov and P. Vieira, Exact Spectrum of PlanarN$$ \mathcal{N} $$ = 4 Supersymmetric Yang-Mills Theory: Konishi Dimension at Any Coupling, Phys. Rev. Lett.104 (2010) 211601 [arXiv:0906.4240] [INSPIRE].
12. G. Arutyunov, S. Frolov and A. Sfondrini, Exceptional Operators in N = 4 super Yang-Mills, JHEP09 (2012) 006 [arXiv:1205.6660] [INSPIRE].
13. S. Frolov, Konishi operator at intermediate coupling, J. Phys.A 44 (2011) 065401 [arXiv:1006.5032] [INSPIRE].
14. N. Gromov, D. Serban, I. Shenderovich and D. Volin, Quantum folded string and integrability: From finite size effects to Konishi dimension, JHEP08 (2011) 046 [arXiv:1102.1040] [INSPIRE].
15. S. Frolov, Scaling dimensions from the mirror TBA, J. Phys.A 45 (2012) 305402 [arXiv:1201.2317] [INSPIRE].
16. R. Roiban and A.A. Tseytlin, Semiclassical string computation of strong-coupling corrections to dimensions of operators in Konishi multiplet, Nucl. Phys.B 848 (2011) 251 [arXiv:1102.1209] [INSPIRE].
17. B.C. Vallilo and L. Mazzucato, The Konishi multiplet at strong coupling, JHEP12 (2011) 029 [arXiv:1102.1219] [INSPIRE].
18. S. Frolov, M. Heinze, G. Jorjadze and J. Plefka, Static gauge and energy spectrum of single-mode strings in AdS5 × S5, J. Phys.A 47 (2014) 085401 [arXiv:1310.5052] [INSPIRE].
19. N. Gromov, V. Kazakov, S. Leurent and D. Volin, Quantum spectral curve for AdS5/CFT4, Phys. Rev. Lett.112 (2014) 011602 [arXiv:1305.1939] [INSPIRE].
20. N. Gromov, V. Kazakov, S. Leurent and D. Volin, Quantum spectral curve for arbitrary state/operator in AdS5/CFT4, arXiv:1405.4857 [INSPIRE].
21. N. Gromov, F. Levkovich-Maslyuk and G. Sizov, Analytic Solution of Bremsstrahlung TBA II: Turning on the Sphere Angle, JHEP10 (2013) 036 [arXiv:1305.1944] [INSPIRE].
22. D. Volin, to appear.
23. B. Basso, An exact slope for AdS/CFT, arXiv:1109.3154 [INSPIRE].
24. B. Basso, Scaling dimensions at small spin in N = 4 SYM theory, arXiv:1205.0054 [INSPIRE].
25. N. Gromov, On the Derivation of the Exact Slope Function, JHEP02 (2013) 055 [arXiv:1205.0018] [INSPIRE].
26. M. Beccaria and A.A. Tseytlin, More about ‘short’ spinning quantum strings, JHEP07 (2012) 089 [arXiv:1205.3656] [INSPIRE].
27. M. Beccaria, S. Giombi, G. Macorini, R. Roiban and A.A. Tseytlin, ’Short’ spinning strings and structure of quantum AdS5 × S5spectrum, Phys. Rev.D 86 (2012) 066006 [arXiv:1203.5710] [INSPIRE].
28. M. Beccaria, C. Ratti and A.A. Tseytlin, Leading quantum correction to energy of ‘short’ spiky strings, J. Phys.A 45 (2012) 155401 [arXiv:1201.5033] [INSPIRE].
29. A. Tirziu and A.A. Tseytlin, Quantum corrections to energy of short spinning string in AdS5, Phys. Rev.D 78 (2008) 066002 [arXiv:0806.4758] [INSPIRE].
30. M. Kruczenski and A.A. Tseytlin, Wilson loops T-dual to Short Strings, Nucl. Phys.B 875 (2013) 213 [arXiv:1212.4886] [INSPIRE].
31. R.A. Janik, Twist-two operators and the BFKL regime — nonstandard solutions of the Baxter equation, JHEP11 (2013) 153 [arXiv:1309.2844] [INSPIRE].
32. N. Gromov and V. Kazakov, unpublished (2013).
33. A.V. Kotikov and L.N. Lipatov, DGLAP and BFKL evolution equations in the N = 4 supersymmetric gauge theory, hep-ph/0112346 [INSPIRE].
34. 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].
35. 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.B 632 (2006) 754] [hep-th/0404092] [INSPIRE].
36. S. Moch, J.A.M. Vermaseren and A. Vogt, The Three loop splitting functions in QCD: The Nonsinglet case, Nucl. Phys.B 688 (2004) 101 [hep-ph/0403192] [INSPIRE].
37. M. Staudacher, The Factorized S-matrix of CFT/AdS, JHEP05 (2005) 054 [hep-th/0412188] [INSPIRE].
38. 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].
39. Z. Bajnok, R.A. Janik and T. Lukowski, Four loop twist two, BFKL, wrapping and strings, Nucl. Phys.B 816 (2009) 376 [arXiv:0811.4448] [INSPIRE].
40. 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].
41. V.N. Velizhanin, Twist-2 at five loops: Wrapping corrections without wrapping computations, JHEP06 (2014) 108 [arXiv:1311.6953] [INSPIRE].
42. L. Freyhult, Review of AdS/CFT Integrability, Chapter III.4: Twist States and the cusp Anomalous Dimension, Lett. Math. Phys.99 (2012) 255 [arXiv:1012.3993] [INSPIRE].
43. D. Maitre, HPL, a mathematica implementation of the harmonic polylogarithms, Comput. Phys. Commun.174 (2006) 222 [hep-ph/0507152] [INSPIRE].
44. D. Maitre, Extension of HPL to complex arguments, Comput. Phys. Commun.183 (2012) 846 [hep-ph/0703052] [INSPIRE].
45. S. Leurent and D. Volin, Mathematica packages for working with zeta functions and FiNLIE-based weak coupling expansion, http://people.kth.se/∼dmytrov/konishi8.zip.
46. S. Leurent and D. Volin, Multiple zeta functions and double wrapping in planar N = 4 SYM, Nucl. Phys.B 875 (2013) 757 [arXiv:1302.1135] [INSPIRE].
47. J. Ablinger, A Computer Algebra Toolbox for Harmonic Sums Related to Particle Physics, arXiv:1011.1176 [INSPIRE].
48. J. Ablinger, Computer Algebra Algorithms for Special Functions in Particle Physics, Ph.D. Thesis, Johannes Kepler University, Linz Austria (2012).
49. J. Ablinger, J. Blümlein and C. Schneider, Analytic and Algorithmic Aspects of Generalized Harmonic Sums and Polylogarithms, arXiv:1302.0378.
50. 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].
51. J. Blümlein, Structural Relations of Harmonic Sums and Mellin Transforms up to Weight w = 5, Comput. Phys. Commun.180 (2009) 2218 [arXiv:0901.3106] [INSPIRE].
52. E. Remiddi and J.A.M. Vermaseren, Harmonic polylogarithms, Int. J. Mod. Phys.A 15 (2000) 725 [hep-ph/9905237] [INSPIRE].
53. J.A.M. Vermaseren, Harmonic sums, Mellin transforms and integrals, Int. J. Mod. Phys.A 14 (1999) 2037 [hep-ph/9806280] [INSPIRE].
54. M. Beccaria, Anomalous dimensions at twist-3 in the sl(2) sector of N = 4 SYM, JHEP06 (2007) 044 [arXiv:0704.3570] [INSPIRE].
55. M. Beccaria, V. Forini, T. Lukowski and S. Zieme, Twist-three at five loops, Bethe Ansatz and wrapping, JHEP03 (2009) 129 [arXiv:0901.4864] [INSPIRE].
56. V.N. Velizhanin, Six-Loop Anomalous Dimension of Twist-Three Operators in N = 4 SYM, JHEP11 (2010) 129 [arXiv:1003.4717] [INSPIRE].
57. M. Beccaria and F. Catino, Sum rules for higher twist sl(2) operators in N = 4 SYM, JHEP06 (2008) 103 [arXiv:0804.3711] [INSPIRE].
58. A.V. Belitsky, G.P. Korchemsky and R.S. Pasechnik, Fine structure of anomalous dimensions in N = 4 super Yang-Mills theory, Nucl. Phys.B 809 (2009) 244 [arXiv:0806.3657] [INSPIRE].
59. N. Beisert, B. Eden and M. Staudacher, Transcendentality and Crossing, J. Stat. Mech.0701 (2007) P01021 [hep-th/0610251] [INSPIRE].
60. N. Dorey, D.M. Hofman and J.M. Maldacena, On the Singularities of the Magnon S-matrix, Phys. Rev.D 76 (2007) 025011 [hep-th/0703104] [INSPIRE].
61. N. Beisert, R. Hernandez and E. Lopez, A Crossing-symmetric phase for AdS5 × S5strings, JHEP11 (2006) 070 [hep-th/0609044] [INSPIRE].
62. P. Vieira and D. Volin, Review of AdS/CFT Integrability, Chapter III.3: The Dressing factor, Lett. Math. Phys.99 (2012) 231 [arXiv:1012.3992] [INSPIRE].
63. http://www.cecm.sfu.ca/projects/EZFace/index.html.
64. N. Gromov and S. Valatka, Deeper Look into Short Strings, JHEP03 (2012) 058 [arXiv:1109.6305] [INSPIRE].
65. T. Regge, Introduction to complex orbital momenta, Nuovo Cim.14 (1959) 951 [INSPIRE].
66. V. Gribov, The theory of complex angular momenta: Gribov lectures on theoretical physics, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge U.K. (2003).
67. L.N. Lipatov, Reggeization of the Vector Meson and the Vacuum Singularity in Nonabelian Gauge Theories, Sov. J. Nucl. Phys.23 (1976) 338 [Yad. Fiz.23 (1976) 642] [INSPIRE].
68. E.A. Kuraev, L.N. Lipatov and V.S. Fadin, The Pomeranchuk Singularity in Nonabelian Gauge Theories, Sov. Phys. JETP45 (1977) 199 [Zh. Eksp. Teor. Fiz.72 (1977) 377] [INSPIRE].
69. I.I. Balitsky and L.N. Lipatov, The Pomeranchuk Singularity in Quantum Chromodynamics, Sov. J. Nucl. Phys.28 (1978) 822 [Yad. Fiz.28 (1978) 1597] [INSPIRE].
70. R.C. Brower, J. Polchinski, M.J. Strassler and C.-I. Tan, The Pomeron and gauge/string duality, JHEP12 (2007) 005 [hep-th/0603115] [INSPIRE].
71. 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.B 685 (2004) 405] [hep-ph/0208220] [INSPIRE].
72. M.S. Costa, V. Goncalves and J. Penedones, Conformal Regge theory, JHEP12 (2012) 091 [arXiv:1209.4355] [INSPIRE].
73. A.V. Kotikov and L.N. Lipatov, Pomeron in the N = 4 supersymmetric gauge model at strong couplings, Nucl. Phys.B 874 (2013) 889 [arXiv:1301.0882] [INSPIRE].
74. R.C. Brower, M. Costa, M. Djuric, T. Raben and C.-I. Tan, Conformal Pomeron and Odderon in Strong Coupling, arXiv:1312.1419 [INSPIRE].
75. S.E. Derkachov, G.P. Korchemsky, J. Kotanski and A.N. Manashov, Noncompact Heisenberg spin magnets from high-energy QCD. 2. Quantization conditions and energy spectrum, Nucl. Phys.B 645 (2002) 237 [hep-th/0204124] [INSPIRE].
76. 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].
77. Z. Bajnok et al., The spectrum of tachyons in AdS/CFT, JHEP03 (2014) 055 [arXiv:1312.3900] [INSPIRE].
78. Z. Bajnok, R.I. Nepomechie, L. Palla and R. Suzuki, Y -system for Y = 0 brane in planar AdS/CFT, JHEP08 (2012) 149 [arXiv:1205.2060] [INSPIRE].
79. D. Correa, J. Maldacena and A. Sever, The quark anti-quark potential and the cusp anomalous dimension from a TBA equation, JHEP08 (2012) 134 [arXiv:1203.1913] [INSPIRE].
80. N. Drukker, Integrable Wilson loops, JHEP10 (2013) 135 [arXiv:1203.1617] [INSPIRE].
81. M. Kim, Spectral curve for gamma-deformed AdS/CFT, arXiv:1401.4032 [INSPIRE].
82. N. Gromov and F. Levkovich-Maslyuk, Y-system and β-deformed N = 4 super-Yang-Mills, J. Phys.A 44 (2011) 015402 [arXiv:1006.5438] [INSPIRE].
83. G. Arutyunov, M. de Leeuw and S.J. van Tongeren, Twisting the Mirror TBA, JHEP02 (2011) 025 [arXiv:1009.4118] [INSPIRE].
84. M. de Leeuw and S.J. van Tongeren, The spectral problem for strings on twisted AdS5 × S5, Nucl. Phys.B 860 (2012) 339 [arXiv:1201.1451] [INSPIRE].
85. G. Arutyunov, M. de Leeuw and S.J. van Tongeren, The Quantum Deformed Mirror TBA II, JHEP02 (2013) 012 [arXiv:1210.8185] [INSPIRE].
86. G. Arutyunov, M. de Leeuw and S.J. van Tongeren, The Quantum Deformed Mirror TBA I, JHEP10 (2012) 090 [arXiv:1208.3478] [INSPIRE].
87. J. Bagger and N. Lambert, Gauge symmetry and supersymmetry of multiple M2-branes, Phys. Rev.D 77 (2008) 065008 [arXiv:0711.0955] [INSPIRE].
88. O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP10 (2008) 091 [arXiv:0806.1218] [INSPIRE].
89. O. Aharony, O. Bergman and D.L. Jafferis, Fractional M2-branes, JHEP11 (2008) 043 [arXiv:0807.4924] [INSPIRE].
90. A. Kapustin, B. Willett and I. Yaakov, Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter, JHEP03 (2010) 089 [arXiv:0909.4559] [INSPIRE].
91. N. Drukker, M. Mariño and P. Putrov, From weak to strong coupling in ABJM theory, Commun. Math. Phys.306 (2011) 511 [arXiv:1007.3837] [INSPIRE].
92. N. Drukker, M. Mariño and P. Putrov, Nonperturbative aspects of ABJM theory, JHEP11 (2011) 141 [arXiv:1103.4844] [INSPIRE].
93. N. Gromov and P. Vieira, The all loop AdS4/CFT3 Bethe ansatz, JHEP01 (2009) 016 [arXiv:0807.0777] [INSPIRE].
94. N. Gromov and F. Levkovich-Maslyuk, Y-system, TBA and Quasi-Classical strings in AdS4 × CP3, JHEP06 (2010) 088 [arXiv:0912.4911] [INSPIRE].
95. D. Bombardelli, D. Fioravanti and R. Tateo, TBA and Y-system for planar AdS4/CFT3, Nucl. Phys.B 834 (2010) 543 [arXiv:0912.4715] [INSPIRE].
96. A. Cavaglià, D. Fioravanti, N. Gromov and R. Tateo, The Quantum Spectral Curve of the ABJM theory, Phys. Rev. Lett.113 (2014) 021601 [arXiv:1403.1859] [INSPIRE].