Multiple zeta functions and double wrapping in planar N=4 SYM

Nuclear Physics B

Volumn 875, Issue 3, 2013, Pages 757-789

  Leurent, Sébastien ^a   Volin, Dmytro ^b,c  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

^c BOGOLYUBOV INSTITUTE FOR THEORETICAL PHYSICS   (Ukraine)

Author keywords

AdS CFT correspondence; FiNLIE; Integrability; Perturbative quantum field theory; Y system

Indexed keywords

EID: 84883187860     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nuclphysb.2013.07.020     Document Type: Article

References (82)

1. Beisert N., Ahn C., Alday L.F., Bajnok Z., Drummond J.M., et al. Review of AdS/CFT integrability: An overview. Lett. Math. Phys. 2012, 99:3-32. arxiv:1012.3982, 10.1007/s11005-011-0529-2.
2. Ambjorn J., Janik R.A., Kristjansen C. Wrapping interactions and a new source of corrections to the spin-chain/string duality. Nucl. Phys. B 2006, 736:288-301. arxiv:hep-th/0510171, 10.1016/j.nuclphysb.2005.12.007.
3. Beisert N., Staudacher M. Long-range PSU(2, 2|4) Bethe Ansaetze for gauge theory and strings. Nucl. Phys. B 2005, 727:1-62. arxiv:hep-th/0504190, 10.1016/j.nuclphysb.2005.06.038.
4. Beisert N., Eden B., Staudacher M. Transcendentality and crossing. J. Stat. Mech. 2007, 0701:P021. arxiv:hep-th/0610251.
5. Gromov N., Kazakov V., Vieira P. Exact spectrum of anomalous dimensions of planar N=4 supersymmetric Yang-Mills theory. Phys. Rev. Lett. 2009, 103:131601. arxiv:0901.3753, 10.1103/PhysRevLett.103.131601.
6. Gromov N., Kazakov V., Vieira P. Exact spectrum of planar N=4 supersymmetric Yang-Mills theory: Konishi dimension at any coupling. Phys. Rev. Lett. 2010, 104:211601. arxiv:0906.4240, 10.1103/PhysRevLett.104.211601.
7. Frolov S. Konishi operator at intermediate coupling. J. Phys. A 2011, 44:065401. arxiv:1006.5032, 10.1088/1751-8113/44/6/065401.
8. Frolov S. Scaling dimensions from the mirror TBA. J. Phys. A 2012, 45:305402. arxiv:1201.2317, 10.1088/1751-8113/45/30/305402.
9. Gromov N., Serban D., Shenderovich I., Volin D. Quantum folded string and integrability: From finite size effects to Konishi dimension. JHEP 2011, 2011:1-23. arxiv:1102.1040.
10. Gromov N., Valatka S. Deeper look into short strings. JHEP 2012, 1203:058. arxiv:1109.6305.
11. 5: strong-coupling corrections to dimension of Konishi operator. JHEP 2009, 0911:013. arxiv:0906.4294, 10.1088/1126-6708/2009/11/013.
12. Roiban R., Tseytlin A. Semiclassical string computation of strong-coupling corrections to dimensions of operators in Konishi multiplet. Nucl. Phys. B 2011, 848:251-267. arxiv:1102.1209, 10.1016/j.nuclphysb.2011.02.016.
13. Vallilo B.C., Mazzucato L. The Konishi multiplet at strong coupling. Journal of High Energy Physics 2011, 2011:1-9. arxiv:1102.1219, 10.1007/JHEP12(2011)029.
14. Bajnok Z., Janik R.A. Four-loop perturbative Konishi from strings and finite size effects for multiparticle states. Nucl. Phys. B 2009, 807:625-650. arxiv:0807.0399, 10.1016/j.nuclphysb.2008.08.020.
15. Bajnok Z., Hegedus A., Janik R.A., Lukowski T. Five loop Konishi from AdS/CFT. Nucl. Phys. B 2010, 827:426-456. arxiv:0906.4062, 10.1016/j.nuclphysb.2009.10.015.
16. Arutyunov G., Frolov S., Suzuki R. Five-loop Konishi from the mirror TBA. JHEP 2010, 1004:069. arxiv:1002.1711, 10.1007/JHEP04(2010)069.
17. Balog J., Hegedus A. 5-loop Konishi from linearized TBA and the XXX magnet. JHEP 2010, 1006:080. arxiv:1002.4142, 10.1007/JHEP06(2010)080.
18. Fiamberti F., Santambrogio A., Sieg C., Zanon D. Wrapping at four loops in N=4 SYM. Phys. Lett. B 2008, 666:100-105. arxiv:0712.3522, 10.1016/j.physletb.2008.06.061.
19. Fiamberti F., Santambrogio A., Sieg C., Zanon D. Anomalous dimension with wrapping at four loops in N=4 SYM. Nucl. Phys. B 2008, 805:231-266. arxiv:0806.2095, 10.1016/j.nuclphysb.2008.07.014.
20. Velizhanin V. The four-loop anomalous dimension of the Konishi operator in N=4 supersymmetric Yang-Mills theory. JETP Lett. 2009, 89:6-9. arxiv:0808.3832, 10.1134/S0021364009010020.
21. Eden B., Heslop P., Korchemsky G.P., Smirnov V.A., Sokatchev E. Five-loop Konishi in N=4 SYM. Nucl. Phys. B 2012, 862:123-166. arxiv:1202.5733, 10.1016/j.nuclphysb.2012.04.015.
22. Bajnok Z., Janik R.A., Lukowski T. Four loop twist two, BFKL, wrapping and strings. Nucl. Phys. B 2009, 816:376-398. arxiv:0811.4448, 10.1016/j.nuclphysb.2009.02.005.
23. Lukowski T., Rej A., Velizhanin V.N. Five-loop anomalous dimension of twist-two operators. Nucl. Phys. B 2010, 831:105-132. arxiv:0912.1624, 10.1016/j.nuclphysb.2010.01.008.
24. Balog J., Hegedus A. The Bajnok-Janik formula and wrapping corrections. JHEP 2010, 1009:107. arxiv:1003.4303, 10.1007/JHEP09(2010)107.
25. Kotikov A.V., Lipatov L.N., Rej A., Staudacher M., Velizhanin V.N. Dressing and wrapping. J. Stat. Mech. 2007, 0710:P10003. arxiv:0704.3586, 10.1088/1742-5468/2007/10/P10003.
26. Leurent S., Serban D., Volin D. Six-loop Konishi anomalous dimension from the Y system. Phys. Rev. Lett. 2012, 109:241601. arxiv:1209.0749, 10.1103/PhysRevLett.109.241601.
27. Bajnok Z., Janik R.A. Six and seven loop Konishi from Luscher corrections. JHEP 2012, 1211:002. arxiv:1209.0791, 10.1007/JHEP11(2012)002.
28. Arutyunov G., Frolov S., van Tongeren S.J. Bound states in the mirror TBA. JHEP 2012, 1202:014. arxiv:1111.0564, 10.1007/JHEP02(2012)014.
29. Arutyunov G., Frolov S., Sfondrini A. Exceptional operators in N=4 super Yang-Mills. JHEP 2012, 1209:006. arxiv:1205.6660, 10.1007/JHEP09(2012)006.
30. Gromov N., Levkovich-Maslyuk F. Y-system and β-deformed N=4 super-Yang-Mills. J. Phys. A 2011, 44:015402. arxiv:1006.5438, 10.1088/1751-8113/44/1/015402.
31. Arutyunov G., de Leeuw M., van Tongeren S.J. Twisting the mirror TBA. JHEP 2011, 1102:025. 10.1007/JHEP02(2011)025.
32. Bajnok Z., el Deeb O. 6-loop anomalous dimension of a single impurity operator from AdS/CFT and multiple zeta values. JHEP 2011, 1101:054. arxiv:1010.5606, 10.1007/JHEP01(2011)054.
33. Ahn C., Bajnok Z., Bombardelli D., Nepomechie R.I. TBA, NLO Luscher correction, and double wrapping in twisted AdS/CFT. JHEP 2011, 1112:059. arxiv:1108.4914, 10.1007/JHEP12(2011)059.
34. 5. Nucl. Phys. B 2012, 860:339-376. 10.1016/j.nuclphysb.2012.03.004.
35. Arutyunov G., de Leeuw M., van Tongeren S.J. The quantum deformed mirror TBA I. JHEP 2012, 1210:090. arxiv:1208.3478, 10.1007/JHEP10(2012)090.
36. Arutyunov G., de Leeuw M., van Tongeren S.J. The quantum deformed mirror TBA II. JHEP 2013, 1302:012. arxiv:1210.8185, 10.1007/JHEP02(2013)012.
37. Correa D., Maldacena J., Sever A. The quark anti-quark potential and the cusp anomalous dimension from a TBA equation. JHEP 2012, 1208:134. arxiv:1203.1913, 10.1007/JHEP08(2012)134.
38. Drukker N. Integrable Wilson loops arxiv:1203.1617.
39. Gromov N., Sever A. Analytic solution of bremsstrahlung TBA. JHEP 2012, 1211:075. arxiv:1207.5489, 10.1007/JHEP11(2012)075.
40. Basso B. An exact slope for AdS/CFT arxiv:1109.3154.
41. Casteill P.Y., Kristjansen C. The strong coupling limit of the scaling function from the quantum string Bethe Ansatz. Nucl. Phys. B 2007, 785:1-18. arxiv:0705.0890, 10.1016/j.nuclphysb.2007.06.011.
42. Gromov N. Generalized scaling function at strong coupling. JHEP 2008, 0811:085. arxiv:0805.4615, 10.1088/1126-6708/2008/11/085.
43. Volin D. The 2-loop generalized scaling function from the BES/FRS equation arxiv:0812.4407.
44. Basso B., Korchemsky G.P., Kotanski J. Cusp anomalous dimension in maximally supersymmetric Yang-Mills theory at strong coupling. Phys. Rev. Lett. 2008, 100:091601. arxiv:0708.3933, 10.1103/PhysRevLett.100.091601.
45. Kostov I., Serban D., Volin D. Functional BES equation. JHEP 2008, 0808:101. arxiv:0801.2542, 10.1088/1126-6708/2008/08/101.
46. A. Hegedus, private communication.
47. Z. Bajnok, private communication.
48. Bombardelli D., Fioravanti D., Tateo R. Thermodynamic Bethe Ansatz for planar AdS/CFT: A proposal. J. Phys. A 2009, 42:375401. arxiv:0902.3930.
49. Gromov N., Kazakov V., Kozak A., Vieira P. Exact spectrum of anomalous dimensions of planar N=4 supersymmetric Yang-Mills theory: TBA and excited states. Lett. Math. Phys. 2010, 91:265-287. arxiv:0902.4458, 10.1007/s11005-010-0374-8.
50. 5 mirror model. JHEP 2009, 0905:068. arxiv:0903.0141, 10.1088/1126-6708/2009/05/068.
51. 4 correspondence. Nucl. Phys. B 2011, 843:302-343. arxiv:1005.3016, 10.1016/j.nuclphysb.2010.09.015.
52. 5 mirror TBA equations from Y-system and discontinuity relations. JHEP 2011, 1108:095. arxiv:1104.4054, 10.1007/JHEP08(2011)095.
53. Gromov N., Kazakov V., Leurent S., Volin D. Solving the AdS/CFT Y-system. JHEP 2012, 1207:023. arxiv:1110.0562, 10.1007/JHEP07(2012)023.
54. Krichever I., Lipan O., Wiegmann P., Zabrodin A. Quantum integrable models and discrete classical Hirota equations. Commun. Math. Phys. 1997, 188:267-304. arxiv:hep-th/9604080, 10.1007/s002200050165.
55. Gromov N., Kazakov V., Tsuboi Z. PSU(2, 2|4) character of quasiclassical AdS/CFT. JHEP 2010, 1007:097. arxiv:1002.3981, 10.1007/JHEP07(2010)097.
56. Gromov N., Kazakov V., Leurent S., Tsuboi Z. Wronskian solution for AdS/CFT Y-system. JHEP 2011, 1101:155. arxiv:1010.2720, 10.1007/JHEP01(2011)155.
57. Tsuboi Z. Solutions of the T-system and Baxter equations for supersymmetric spin chains. Nucl. Phys. B 2010, 826:399-455. arxiv:0906.2039, 10.1016/j.nuclphysb.2009.08.009.
58. Tsuboi Z. Wronskian solutions of the T, Q and Y-systems related to infinite dimensional unitarizable modules of the general linear superalgebra gl(M|N) arxiv:1109.5524.
59. Volin D. String hypothesis for gl(n|m) spin chains: a particle/hole democracy. Lett. Math. Phys. 2012, 102:1-29. arxiv:1012.3454, 10.1007/s11005-012-0570-9.
60. 4 arxiv:1305.1939.
61. Leurent S., Volin D. Mathematica packages for working with zeta functions and FiNLIE-based weak coupling expansion http://people.kth.se/~dmytrov/konishi8.zip.
62. Zudilin W. Algebraic relations for multiple zeta values. Uspekhi Mat. Nauk 2003, 58(1):3-32.
63. Waldschmidt M. Valeurs zêta multiples. Une introduction. Journal de théorie des nombres de Bordeaux 2000, 12(4):581-595. 10.5802/jtnb.298.
64. Ablinger J., Blumlein J., Schneider C. Analytic and algorithmic aspects of generalized harmonic sums and polylogarithms arxiv:1302.0378.
65. Goncharov A. Multiple polylogarithms, cyclotomy and modular complexes. Mathematical Research Letters 1998, 5:497-516.
66. Hoffman M.E. The algebra of multiple harmonic series. Journal of Algebra 1997, 194(2):477-495. 10.1006/jabr.1997.7127.
67. Bailey D.H., Broadhurst D.J. Parallel integer relation detection: Techniques and applications. Math. Comput. 2001, 70(236):1719-1736.
68. Broadhurst D.J., Kreimer D. Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops. Phys. Lett. B 1997, 393:403-412. arxiv:hep-th/9609128, 10.1016/S0370-2693(96)01623-1.
69. Ohno Y. A generalization of the duality and sum formulas on the multiple zeta values. Journal of Number Theory 1999, 74(1):39-43. 10.1006/jnth.1998.2314.
70. Hoffman M.E., Ohno Y. Relations of multiple zeta values and their algebraic expression. J. Algebra 2003, 262:332-347. arxiv:math/0010140.
71. Ihara K., Kaneko M., Zagier D. Derivation and double shuffle relations for multiple zeta values. Compositio Mathematica 2006, 142:307-338. 10.1112/S0010437X0500182X.
72. Blumlein J., Broadhurst D., Vermaseren J. The multiple zeta value data mine. Comput. Phys. Commun. 2010, 181:582-625. 10.1016/j.cpc.2009.11.007.
73. Ablinger J., Blumlein J., Schneider C. Harmonic sums and polylogarithms generated by cyclotomic polynomials. J. Math. Phys. 2011, 52:102301. 10.1063/1.3629472.
74. Gromov N., Kazakov V., Vieira P. Finite volume spectrum of 2d field theories from Hirota dynamics. JHEP 2008, 2009(12):060. arxiv:0812.5091.
75. Kazakov V., Leurent S. Finite size spectrum of SU(N) principal chiral field from discrete Hirota dynamics arxiv:1007.1770.
76. 5 superstring worldsheet S-matrix and crossing symmetry. Phys. Rev. D 2006, 73:086006. arxiv:hep-th/0603038, 10.1103/PhysRevD.73.086006.
77. Volin D. Minimal solution of the AdS/CFT crossing equation. Journal of Physics A: Mathematical and Theoretical 2009, 42(37):372001. arxiv:0904.4929.
78. N. Gromov, private communication.
79. Schnetz O. Single-valued multiple-zeta-values. SFB Colloquium "Novel Methods for Perturbative QFT" May 2013, Humboldt-Universität zu Berlin. http://www.raumzeitmaterie.de/veranstaltungen.php?evt=select&sqn=8970&lang=en.
80. 4 theory to 7 loops and beyond. Int. J. Mod. Phys. C 1995, 6:519-524. arxiv:hep-ph/9504352, 10.1142/S012918319500037X.
81. 4 arxiv:1006.4064.
82. Dorey P., Tateo R. Excited states by analytic continuation of TBA equations. Nucl. Phys. B 1996, 482:639-659. arxiv:hep-th/9607167, 10.1016/S0550-3213(96)00516-0.