Complete 1-loop test of AdS/CFT

Journal of High Energy Physics

Volumn 2008, Issue 4, 2008, Pages

  Gromov, Nikolay ^a,b   Vieira, Pedro ^a,c  

^a LABORATOIRE DE PHYSIQUE STATISTIQUE   (France)

^b StPetersburg INP   (Russian Federation)

^c UNIVERSITY OF PORTO   (Portugal)

Author keywords

AdS CFT correspondence; Bethe ansatz; Integrable field theories

Indexed keywords

EID: 44449151242     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2008/04/046     Document Type: Article

References (81)

1. H. Bethe, On the theory of metals. 1. Eigenvalues and eigenfunctions for the linear atomic chain 1931 Z. Phys. 71 205
2. M. Lüscher, Volume dependence of the energy spectrum in massive quantum field theories. 1. Stable particle states 1986 Comm. Math. Phys. 104 177
3. T.R. Klassen and E. Melzer, On the relation between scattering amplitudes and finite size mass corrections in QFT 1991 Nucl. Phys. B 362 329
4. B. Sutherland, Low-lying eigenstates of the one-dimensional Heisenberg ferromagnet for any magnetization and momentum 1995 Phys. Rev. Lett. 74 816
5. N. Beisert, J.A. Minahan, M. Staudacher and K. Zarembo, Stringing spins and spinning strings 2003 J. High Energy Phys. JHEP09(2003)010 [hep-th/0306139]
6. O. Babelon, D. Bernard and M. Talon, Introduction to classical integrable systems (Cambridge University Press, Cambridge) U.K. (2003)
7. E.D. Belokolos, A.I. Bobenko, V.Z. Enolskii, A.R. Its and V.B. Matveev, Algebrogeometric approach to nonlinear integrable equations Springer, Berlin Germany (1994)
8. V.A. Kazakov, A. Marshakov, J.A. Minahan and K. Zarembo, Classical / quantum integrability in AdS/CFT 2004 J. High Energy Phys. JHEP05(2004)024 [hep-th/0402207]
9. 5 2006 Comm. Math. Phys. 263 659 [hep-th/0502226]
10. N. Gromov, V. Kazakov, K. Sakai and P. Vieira, Strings as multi-particle states of quantum σ-models 2007 Nucl. Phys. B 764 15 [hep-th/0603043]
11. N. Beisert and A.A. Tseytlin, On quantum corrections to spinning strings and Bethe equations 2005 Phys. Lett. B 629 102 [hep-th/0509084]
12. 5 and Bethe ansatz: a comparative study 2005 J. High Energy Phys. JHEP09(2005)051 [hep-th/0507189]
13. N. Beisert, A.A. Tseytlin and K. Zarembo, Matching quantum strings to quantum spins: one-loop vs. finite-size corrections 2005 Nucl. Phys. B 715 190 [hep-th/0502173]
14. R. Hernandez, E. Lopez, A. Perianez and G. Sierra, Finite size effects in ferromagnetic spin chains and quantum corrections to classical strings 2005 J. High Energy Phys. JHEP06(2005)011 [hep-th/0502188]
15. N. Beisert and L. Freyhult, Fluctuations and energy shifts in the Bethe ansatz 2005 Phys. Lett. B 622 343 [hep-th/0506243]
16. N. Gromov and V. Kazakov, Double scaling and finite size corrections in SL(2) spin chain, 2006 Nucl. Phys. B 736 199 [hep-th/0510194]
17. P.Y. Casteill and C. Kristjansen, The strong coupling limit of the scaling function from the quantum string Bethe ansatz 2007 Nucl. Phys. B 785 1 [0705.0890]
18. N. Beisert, V.A. Kazakov, K. Sakai and K. Zarembo, Complete spectrum of long operators in N = 4 SYM at one loop 2005 J. High Energy Phys. JHEP07(2005)030 [hep-th/0503200]
19. P.A. Bares, I.M.P. Karmelo, J. Ferrer and P. Horsch, Charge-spin recombination in the one-dimensional supersymmetric t-J model 1992 Phys. Rev. 46 14624
20. c superconductivity [cond-mat/9209002]
21. H. Bethe, Exact solution of an electronic model of superconductivity in (1+1)-dimensions. 1 [cond-mat/9211001]
22. F. Göhmann and A. Seel, A note on the Bethe ansatz solution of the supersymmetric t-J model [cond-mat/0309138]
23. F. Woynarovich, Low energy excited states in a Hubbard chain with on-site attraction 1983 J. Phys. C 16 6593
24. Z. Tsuboi, Analytic Bethe ansatz and functional equations associated with any simple root systems of the Lie superalgebra SL(r+1|s+1), 1998 Physica A 252 565
25. V. Kazakov, A. Sorin and A. Zabrodin, Supersymmetric Bethe ansatz and Baxter equations from discrete Hirota dynamics 2008 Nucl. Phys. B 790 345 [hep-th/0703147]
26. N. Beisert and M. Staudacher, Long-range PSU(2,2|4) Bethe ansaetze for gauge theory and strings 2005 Nucl. Phys. B 727 1 [hep-th/0504190]
27. J.M. Maldacena, The large-N limit of superconformal field theories and supergravity 1998 Adv. Theor. Math. Phys. 2 231 [1999 Int. J. Theor. Phys. 38 1113] [hep-th/9711200]
28. S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from non-critical string theory 1998 Phys. Lett. B 428 105 [hep-th/9802109]
29. E. Witten, Anti-de Sitter space and holography 1998 Adv. Theor. Math. Phys. 2 253 [hep-th/9802150]
30. J.A. Minahan and K. Zarembo, The Bethe-ansatz for N = 4 super Yang-Mills 2003 J. High Energy Phys. JHEP03(2003)013 [hep-th/0212208]
31. N. Beisert, The complete one-loop dilatation operator of N = 4 super Yang-Mills theory 2004 Nucl. Phys. B 676 3 [hep-th/0307015]
32. 5 superstring quantum spectrum from the algebraic curve 2008 Nucl. Phys. B 789 175 [hep-th/0703191]
33. N. Gromov and P. Vieira, Constructing the AdS/CFT dressing factor 2008 Nucl. Phys. B 790 72 [hep-th/0703266]
34. R.A. Janik and T. Lukowski, Wrapping interactions at strong coupling - the giant magnon 2007 Phys. Rev. D 76 126008 [0708.2208]
35. S. Schäfer-Nameki, Exact expressions for quantum corrections to spinning strings 2006 Phys. Lett. B 639 571 [hep-th/0602214]
36. S. Schäfer-Nameki, M. Zamaklar and K. Zarembo, How accurate is the quantum string Bethe ansatz? 2006 J. High Energy Phys. JHEP12(2006)020 [hep-th/0610250]
37. G. Arutyunov, S. Frolov and M. Zamaklar, Finite-size effects from giant magnons 2007 Nucl. Phys. B 778 1 [hep-th/0606126]
38. J. Ambjørn, R.A. Janik and C. Kristjansen, Wrapping interactions and a new source of corrections to the spin-chain/string duality 2006 Nucl. Phys. B 736 288 [hep-th/0510171]
39. S. Schäfer-Nameki and M. Zamaklar, Stringy sums and corrections to the quantum string Bethe ansatz 2005 J. High Energy Phys. JHEP10(2005)044 [hep-th/0509096]
40. R. Hernandez and E. Lopez, Quantum corrections to the string Bethe ansatz 2006 J. High Energy Phys. JHEP07(2006)004 [hep-th/0603204]
41. A. Zabrodin, Backlund transformations for difference Hirota equation and supersymmetric Bethe ansatz [0705.4006]
42. L.D. Faddeev, How algebraic Bethe ansatz works for integrable model [hep-th/9605187]
43. N.Y. Reshetikhin, A method of functional equations in the theory of exactly solvable quantum systems 1983 Lett. Math. Phys. 7 205
44. N.Y. Reshetikhin, Integrable models of quantum one-dimensional magnets with O(N) and Sp(2K) symmetry 1985 Theor. Math. Phys. 63 555 [1985 Teor. Mat. Fiz. 63 347]
45. I. Krichever, O. Lipan, P. Wiegmann and A. Zabrodin, Quantum integrable models and discrete classical Hirota equations 1997 Comm. Math. Phys. 188 267 [hep-th/9604080]
46. 5 2003 Nucl. Phys. B 668 77 [hep-th/0304255]
47. 5 2003 J. High Energy Phys. JHEP07(2003)016 [hep-th/0306130]
48. 5: new integrable system relations 2004 Phys. Rev. D 69 086009 [hep-th/0311004]
49. 5: one-loop correction to energy in SL(2) sector, 2005 J. High Energy Phys. JHEP03(2005)013 [hep-th/0501203]
50. 5 background 1998 Nucl. Phys. B 533 109 [hep-th/9805028]
51. S. Randjbar-Daemi, A. Salam and J.A. Strathdee, Generalized spin systems and σ-models 1993 Phys. Rev. B 48 3190 [hep-th/9210145]
52. M. Kruczenski, Spin chains and string theory 2004 Phys. Rev. Lett. 93 161602 [hep-th/0311203]
53. 5 string theory and low energy expansion of ferromagnetic spin chains 2004 Nucl. Phys. B 692 3 [hep-th/0403120]
54. 5 2002 J. High Energy Phys. JHEP06(2002)007 [hep-th/0204226]
55. T. Bargheer, N. Beisert and N. Gromov, to appear
56. G. Arutyunov, S. Frolov and M. Staudacher, Bethe ansatz for quantum strings 2004 J. High Energy Phys. JHEP10(2004)016 [hep-th/0406256]
57. M. Staudacher, The factorized S-matrix of CFT/AdS 2005 J. High Energy Phys. JHEP05(2005)054 [hep-th/0412188]
58. N. Beisert, The SU(2|2) dynamic S-matrix, [hep-th/0511082]
59. 5 strings 2006 J. High Energy Phys. JHEP11(2006)070 [hep-th/0609044]
60. 5 strings 2007 Mod. Phys. Lett. A 22 415 [hep-th/0606214]
61. 5 superstring worldsheet S-matrix and crossing symmetry 2006 Phys. Rev. D 73 086006 [hep-th/0603038]
62. N. Beisert, B. Eden and M. Staudacher, Transcendentality and crossing 2007 J. Stat. Mech. P01021 [hep-th/0610251]
63. B. Eden and M. Staudacher, Integrability and transcendentality 2006 J. Stat. Mech. P11014 [hep-th/0603157]
64. A.V. Kotikov and L.N. Lipatov, DGLAP and BFKL equations in the N = 4 supersymmetric gauge theory 2003 Nucl. Phys. B 661 19 [Erratum 2004 J. High Energy Phys. B 685 405] [hep-ph/0208220]
65. Z. Bern, M. Czakon, L.J. Dixon, D.A. Kosower and V.A. Smirnov, The four-loop planar amplitude and cusp anomalous dimension in maximally supersymmetric Yang-Mills theory 2007 Phys. Rev. D 75 085010 [hep-th/0610248]
66. N. Beisert, T. McLoughlin and R. Roiban, The four-loop dressing phase of N = 4 SYM 2007 Phys. Rev. D 76 046002 [0705.0321]
67. A.V. Kotikov, L.N. Lipatov, A. Rej, M. Staudacher and V.N. Velizhanin, Dressing and wrapping 2007 J. Stat. Mech. P10003 [0704.3586]
68. N. Dorey, D.M. Hofman and J.M. Maldacena, On the singularities of the magnon S-matrix 2007 Phys. Rev. D 76 025011 [hep-th/0703104]
69. 5 2008 Nucl. Phys. B 791 93 [0707.4254]
70. R. Roiban and A.A. Tseytlin, Strong-coupling expansion of cusp anomaly from quantum superstring 2007 J. High Energy Phys. JHEP11(2007)016 [0709.0681]
71. 5: one-loop scattering amplitudes 2007 J. High Energy Phys. JHEP02(2007)071 [hep-th/0701240]
72. 5 at two loops 2007 J. High Energy Phys. JHEP08(2007)051 [0704.3891]
73. 5 2007 Phys. Rev. D 76 026002 [hep-th/0612079]
74. L. Freyhult, Bethe ansatz and fluctuations in SU(3) Yang-Mills operators, 2004 J. High Energy Phys. JHEP06(2004)010 [hep-th/0405167]
75. L. Freyhult and C. Kristjansen, Finite size corrections to three-spin string duals 2005 J. High Energy Phys. JHEP05(2005)043 [hep-th/0502122]
76. L. Freyhult and C. Kristjansen, A universality test of the quantum string Bethe ansatz 2006 Phys. Lett. B 638 258 [hep-th/0604069]
77. N. Beisert and R. Roiban, Beauty and the twist: the Bethe ansatz for twisted N = 4 SYM 2005 J. High Energy Phys. JHEP08(2005)039 [hep-th/0505187]
78. S.A. Frolov, R. Roiban and A.A. Tseytlin, Gauge-string duality for (non)supersymmetric deformations of N = 4 super Yang-Mills theory 2005 Nucl. Phys. B 731 1 [hep-th/0507021]
79. H.-Y. Chen, N. Dorey and R.F. Lima Matos, Quantum scattering of giant magnons 2007 J. High Energy Phys. JHEP09(2007)106 [0707.0668]
80. D.M. Hofman and J.M. Maldacena, Giant magnons 2006 J. Phys. A: Math. Gen. 39 13095 [hep-th/0604135]
81. N. Beisert, The analytic Bethe ansatz for a chain with centrally extended SU(2|2) symmetry, 2007 J. Stat. Mech. P01017 [nlin/0610017]