Bethe Ansatz solutions for highest states in N = 4 SYM and AdS/CFT duality

Journal of High Energy Physics

Volumn 2006, Issue 9, 2006, Pages

  Beccaria, Matteo ^a,b   Del Debbio, Luigi ^c  

^a UNIVERSITY OF SALENTO   (Italy)

^b INFN SEZIONE DI LECCE   (Italy)

^c UNIVERSITY OF EDINBURGH   (United Kingdom)

Author keywords

AdS CFT Correspondence; Bethe Ansatz; Lattice Integrable Models

Indexed keywords

EID: 33749405545     PISSN: 10298479     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2006/09/025     Document Type: Article

References (58)

1. J.M. Maldacena, The large-N limit of superconformal field theories and supergravity 1998 Adv. Theor. Math. Phys. 2 231 [hep-th/9711200]
2. 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]
3. E. Witten, Anti-de Sitter space and holography 1998 Adv. Theor. Math. Phys. 2 253 [hep-th/9802150]
4. 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]
5. I.R. Klebanov, Tasi lectures: introduction to the AdS/CFT correspondence [hep-th/0009139]
6. 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]
7. N. Beisert, The complete one-loop dilatation operator of N = 4 super Yang-Mills theory 2004 Nucl. Phys. B 676 3 [hep-th/0307015]
8. N. Beisert, The dilatation operator of N = 4 super Yang-Mills theory and integrability 2005 Phys. Rep. 405 1 [hep-th/0407277]
9. M. Staudacher, The factorized S-matrix of CFT/ads 2005 J. High Energy Phys. JHEP05(2005)054 [hep-th/0412188]
10. 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]
11. N. Beisert, V. Dippel and M. Staudacher, A novel long range spin chain and planar N = 4 super Yang-Mills 2004 J. High Energy Phys. JHEP07(2004)075 [hep-th/0405001]
12. A. Rej, D. Serban and M. Staudacher, Planar N = 4 gauge theory and the hubbard model 2006 J. High Energy Phys. JHEP03(2006)018 [hep-th/0512077]
13. J.A. Minahan, Strong coupling from the Hubbard model [hep-th/0603175]
14. M. Beccaria and C. Ortix, Strong coupling anomalous dimensions of N = 4 super Yang-Mills [hep-th/0606138]
15. D. Berenstein, J.M. Maldacena and H. Nastase, Strings in flat space and pp waves from N = 4 super Yang-Mills 2002 J. High Energy Phys. JHEP04(2002)013 [hep-th/0202021]
16. 5: beyond the pp-wave 2003 Nucl. Phys. B 673 3 [hep-th/0307032]
17. C.G. Callan Jr., T. McLoughlin and I.J. Swanson, Holography beyond the Penrose limit 2004 Nucl. Phys. B 694 115 [hep-th/0404007]
18. C.G. Callan Jr., T. McLoughlin and I.J. Swanson, Higher impurity AdS/CFT correspondence in the near-BMN limit 2004 Nucl. Phys. B 700 271 [hep-th/0405153]
19. C.G. Callan Jr., J. Heckman, T. McLoughlin and I.J. Swanson, Lattice super Yang-Mills: a virial approach to operator dimensions 2004 Nucl. Phys. B 701 180 [hep-th/0407096]
20. D. Serban and M. Staudacher, Planar N = 4 gauge theory and the Inozemtsev long range spin chain 2004 J. High Energy Phys. JHEP06(2004)001 [hep-th/0401057]
21. G. Arutyunov, S. Frolov and M. Staudacher, Bethe ansatz for quantum strings 2004 J. High Energy Phys. JHEP10(2004)016 [hep-th/0406256]
22. N. Beisert and A.A. Tseytlin, On quantum corrections to spinning strings and Bethe equations 2005 Phys. Lett. B 629 102 [hep-th/0509084]
23. 5 and Bethe ansatz: a comparative study 2005 J. High Energy Phys. JHEP09(2005)051 [hep-th/0507189]
24. S. Schafer-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]
25. S. Schafer-Nameki, Exact expressions for quantum corrections to spinning strings 2006 Phys. Lett. B 639 571 [hep-th/0602214]
26. 5 2003 Nucl. Phys. B 668 77 [hep-th/0304255]
27. S. Frolov and A.A. Tseytlin, Rotating string solutions: AdS/CFT duality in non-supersymmetric sectors 2003 Phys. Lett. B 570 96 [hep-th/0306143]
28. 5 2006 Int. J. Mod. Phys. A 21 3673 [arXiv:hep-th/0504123]
29. 5 and integrable systems 2003 Nucl. Phys. B 671 3 [hep-th/0307191]
30. 5: new integrable system relations 2004 Phys. Rev. D 69 086009 [hep-th/0311004]
31. 5 2003 J. High Energy Phys. JHEP07(2003)016 [hep-th/0306130]
32. 5 2005 Phys. Rev. D 71 026006 [hep-th/0408187]
33. 5: one-loop correction to energy in SL(2) sector 2005 J. High Energy Phys. JHEP03(2005)013 [hep-th/0501203]
34. R. Hernandez and E. Lopez, Quantum corrections to the string Bethe ansatz 2006 J. High Energy Phys. JHEP07(2006)004 [hep-th/0603204]
35. L. Freyhult and C. Kristjansen, A universality test of the quantum string Bethe ansatz 2006 Phys. Lett. B 638 258 [hep-th/0604069]
36. G. Arutyunov and A.A. Tseytlin, On highest-energy state in the SU(1|1) sector of N = 4 super Yang-Mills theory 2006 J. High Energy Phys. JHEP05(2006)033 [hep-th/0603113]
37. K. Zarembo, Antiferromagnetic operators in N = 4 supersymmetric Yang-Mills theory 2006 Phys. Lett. B 634 552 [hep-th/0512079]
38. G. Feverati, D. Fioravanti, P. Grinza and M. Rossi, On the finite size corrections of anti-ferromagnetic anomalous dimensions in N = 4 SYM 2006 J. High Energy Phys. JHEP05(2006)068 [hep-th/0602189]
39. 5 2002 J. High Energy Phys. JHEP06(2002)007 [hep-th/0204226]
40. 5 2003 Nucl. Phys. B 668 77 [hep-th/0304255]
41. 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]
42. N. Beisert, S. Frolov, M. Staudacher and A.A. Tseytlin, Precision spectroscopy of AdS/CFT 2003 J. High Energy Phys. JHEP10(2003)037 [hep-th/0308117]
43. R. Roiban, A. Tirziu and A.A. Tseytlin, Slow-string limit and 'antiferromagnetic' state in AdS/CFT 2006 Phys. Rev. D 73 066003 [hep-th/0601074]
44. N. Beisert, The SU(2|3) dynamic spin chain 2004 Nucl. Phys. B 682 487 [hep-th/0310252]
45. E. J. Weniger, Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series 1989 Comp. Phys. Rep. 10 189
46. The Newton algorithm is available in the modern packages for symbolic/numerical calculations. A simple description of the Newton algorithm can be found in William T. Vetterling, Brian P. Flannery, Numerical Recipes in C++: The Art of Scientific Computing William H. Press and Saul A. Teukolsky eds., (Cambridge University Press),2 edition, February 2002, ISBN: 0521750334
47. D.M. Hofman and J.M. Maldacena, Giant magnons [hep-th/0604135]
48. N. Dorey, Magnon bound states and the AdS/CFT correspondence [hep-th/0604175]
49. M. Spradlin and A. Volovich, Dressing the giant magnon [hep-th/0607009]
50. N.P. Bobev and R.C. Rashkov, Multispin giant magnons 2006 Phys. Rev. D 74 046011 [hep-th/0607018]
51. 5 [hep-th/0607044]
52. G. Arutyunov, S. Frolov and M. Zamaklar, Finite-size effects from giant magnons [hep-th/0606126]
53. H.Y. Chen, N. Dorey and K. Okamura, Dyonic giant magnons [hep-th/0605155]
54. J.A. Minahan, A. Tirziu and A.A. Tseytlin, Infinite spin limit of semiclassical string states [hep-th/0606145]
55. 5 2006 J. High Energy Phys. JHEP01(2006)078 [hep-th/0508140]
56. 5: solving SU(1|1) sector 2006 J. High Energy Phys. JHEP01(2006)055 [hep-th/0510208]
57. 5 superstring in light-cone gauge and its Bethe equations [hep-th/0603008]
58. Wolfram Research, Inc., Mathematica, Version 5.2, Champaign, IL, 2005