A brief introduction to the Bethe ansatz in N =4 super-Yang-Mills

Journal of Physics A: Mathematical and General

Volumn 39, Issue 41, 2006, Pages 12657-12677

  Minahan, Joseph A ^a,b  

^a HARVARD UNIVERSITY   (United States)

^b UPPSALA UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33749394029     PISSN: 03054470     EISSN: 13616447     Source Type: Journal    
DOI: 10.1088/0305-4470/39/41/S02     Document Type: Article

References (90)

1. Minahan J A and Zarembo K 2003 The Bethe-ansatz for N ≤ 4 super-Yang-Mills J. High Energy Phys. JHEP03(2003)013 (Preprint hep-th/0212208)
2. Maldacena J M 1998 The large N limit of superconformal field theories and supergravity Adv. Theor. Math. Phys. 2 231 (Int. J. Theor. Phys. 38 1113 (1999)) (Preprint hep-th/9711200)
3. Gubser S S, Klebanov I R and Polyakov A M 1998 Gauge theory correglators from non-critical string theory Phys. Lett. B 428 105 (Preprint hep-th/9802109)
4. Witten E 1998 Anti-de sitter space and holography Adv. Theor. Math. Phys. 2 253 (Preprint hep-th/9802150)
5. Beisert N and Staudacher M 2003 The N ≤ 4 SYM integrable super spin chain Nucl. Phys. B 670 439 (Preprint hep-th/0307042)
6. Beisert N, Kristjansen C and Staudacher M 2003 The dilatation operator of N ≤ 4 super-Yang-Mills theory Nucl. Phys. B 664 131 (Preprint hep-th/0303060)
7. Beisert N 2004 The su(2|3) dynamic spin chain Nucl. Phys. B 682 487 (Preprint hep-th/0310252)
8. Beisert N 2005 The dilatation operator of N ≤ 4 super Yang-Mills theory and integrability Phys. Rep. 405 1 (Preprint hep-th/0407277)
9. Peskin M E and Schroeder D V 1995 An Introduction to Quantum Field Theory (Reading, MA: Addison-Wesley)
10. Bethe H 1931 On the theory of metals. 1. Eigenvalues and eigenfunctions for the linear atomic chain Z. Phys. 71 205
11. Berenstein D, Maldacena J M and Nastase H 2002 Strings in flat space and pp waves from N ≤ 4 super Yang Mills J. High Energy Phys. JHEP04(2002)013 (Preprint hep-th/0202021)
12. Beisert N, Minahan J A, Staudacher M and Zarembo K 2003 Stringing spins and spinning strings J. High Energy Phys. JHEP09(2003)010 (Preprint hep-th/0306139)
13. Arutyunov G and Staudacher M 2004 Matching higher conserved charges for strings and spins J. High Energy Phys. JHEP03(2004)004 (Preprint hep-th/0310182)
14. Engquist J, Minahan J A and Zarembo K 2003 Yang-Mills duals for semiclassical strings on AdS(5)× S**5 J. High Energy Phys. JHEP11(2003)063 (Preprint hep-th/0310188)
15. Brezin E, Itzykson C, Parisi G and Zuber J B 1978 Planar diagrams Commun. Math. Phys. 59 35
16. Sutherland B 1995 Phys. Rev. Lett. 74 816
17. Dhar A and Shastry B S 2000 Preprint cond-mat/0005397
18. Kazakov V A, Marshakov A, Minahan J A and Zarembo K 2004 Classical/quantum integrability in AdS/CFT J. High Energy Phys. JHEP05(2004)024 (Preprint hep-th/0402207)
19. Bena I, Polchinski J and Roiban R 2004 Hidden symmetries of the AdS(5)× S**5 superstring Phys. Rev. D 69 046002 (Preprint hep-th/0305116)
20. Frolov S and Tseytlin A A 2003 Multi-spin string solutions in AdS(5)× S**5 Nucl. Phys. B 668 77 (Preprint hep-th/0304255)
21. Arutyunov G, Russo J and Tseytlin A A 2004 Spinning strings in AdS(5)× S**5: new integrable system relations Phys. Rev. D 69 086009 (Preprint hep-th/0311004)
22. Serban D and Staudacher M 2004 Planar N ≤ 4 gauge theory and the Inozemtsev long range spin chain J. High Energy Phys. JHEP06(2004)001 (Preprint hep-th/0401057)
23. Aharony O, Gubser S S, Maldacena J M, Ooguri H and Oz Y 2000 Large N field theories, string theory and gravity Phys. Rep. 323 183 (Preprint hep-th/9905111)
24. Callan C G, Lee H K, McLoughlin T, Schwarz J H, Swanson I and Wu X 2003 Quantizing string theory in AdS(5)× S**5: beyond the pp-wave Nucl. Phys. B 673 3 (Preprint hep-th/0307032)
25. Lipatov L N 1993 High-energy asymptotics of multicolor QCD and exactly solvable lattice models Preprint hep-th/9311037
26. Faddeev L D and Korchemsky G P 1995 High-energy QCD as a completely integrable model Phys. Lett. B 342 311 (Preprint hep-th/9404173)
27. Braun V M, Derkachov S E and Manashov A N 1998 Integrability of three-particle evolution equations in QCD Phys. Rev. Lett. 81 2020 (Preprint hep-ph/9805225)
28. Braun V M, Derkachov S E, Korchemsky G P and Manashov A N 1999 Baryon distribution amplitudes in QCD Nucl. Phys. B 553 355 (Preprint hep-ph/9902375)
29. Belitsky A V 2000 Renormalization of twist-three operators and integrable lattice models Nucl. Phys. B 574 407 (Preprint hep-ph/9907420)
30. Belitsky A V, Gorsky A S and Korchemsky G P 2003 Gauge/string duality for QCD conformal operators Nucl. Phys. B 667 3 (Preprint hep-th/0304028)
31. Belitsky A V, Braun V M, Gorsky A S and Korchemsky G P 2004 Integrability in QCD and beyond Int. J. Mod. Phys. A 19 4715 (Preprint hep-th/0407232)
32. Vogt A, Moch S and Vermaseren J A M 2004 The three-loop splitting functions in QCD: the singlet case Nucl. Phys. B 691 129 (Preprint hep-ph/0404111)
33. Kotikov A V, Lipatov L N, Onishchenko A I and Velizhanin V N 2004 Three-loop universal anomalous dimension of the Wilson operators in N ≤ 4 SUSY Yang-Mills model Phys. Lett. B 595 521
34. Kotikov A V, Lipatov L N, Onishchenko A I and Velizhanin V N 2006 Three-loop universal anomalous dimension of the Wilson operators in N ≤ 4 SUSY Yang-Mills model Phys. Lett. B 632 754 (erratum) (Preprint hep-th/0404092)
35. Eden B, Jarczak C and Sokatchev E 2005 A three-loop test of the dilatation operator in N ≤ 4 SYM Nucl. Phys. B 712 157 (Preprint hep-th/0409009)
36. Gubser S S, Klebanov I R and Polyakov A M 2002 A semi-classical limit of the gauge/string correspondence Nucl. Phys. B 636 99 (Preprint hep-th/0204051)
37. Frolov S and Tseytlin A A 2002 Semiclassical quantization of rotating superstring in AdS(5)× S(5) J. High Energy Phys. JHEP06(2002)007 (Preprint hep-th/0204226)
38. Russo J G 2002 Anomalous dimensions in gauge theories from rotating strings in AdS(5)× S(5) J. High Energy Phys. JHEP06(2002)038 (Preprint hep-th/0205244)
39. Minahan J A 2003 Circular semiclassical string solutions on AdS(5)× S**5 Nucl. Phys. B 648 203 (Preprint hep-th/0209047)
40. Arutyunov G, Frolov S, Russo J and Tseytlin A A 2003 Spinning strings in AdS(5)× S**5 and integrable systems Nucl. Phys. B 671 3 (Preprint hep-th/0307191)
41. Beisert N, Frolov S, Staudacher M and Tseytlin A A 2003 Precision spectroscopy of AdS/CFT J. High Energy Phys. JHEP10(2003)037 (Preprint hep-th/0308117)
42. Kruczenski M 2005 Spiky strings and single trace operators in gauge theories J. High Energy Phys. JHEP08(2005)014 (Preprint hep-th/0410226)
43. Mandal G, Suryanarayana N V and Wadia S R 2002 Aspects of semiclassical strings in AdS(5) Phys. Lett. B 543 81 (Preprint hep-th/0206103)
44. Dolan L, Nappi C R and Witten E 2003 A relation between approaches to integrability in superconformal Yang-Mills theory J. High Energy Phys. JHEP10(2003)017 (Preprint hep-th/0308089)
45. Minahan J A 2005 The SU(2) sector in AdS/CFT Fortsch. Phys. 53 828 (Preprint hep-th/0503143)
46. Kazakov V A and Zarembo K 2004 Classical/quantum integrability in non-compact sector of AdS/CFT J. High Energy Phys. JHEP10(2004)060 (Preprint hep-th/0410105)
47. Beisert N, Kazakov V A and Sakai K 2006 Algebraic curve for the SO(6) sector of AdS/CFT Commun. Math. Phys. 263 611 (Preprint hep-th/0410253)
48. Schafer-Nameki S 2005 The algebraic curve of 1-loop planar N ≤ 4 SYM Nucl. Phys. B 714 3 (Preprint hep-th/0412254)
49. Beisert N, Kazakov V A, Sakai K and Zarembo K 2006 The algebraic curve of classical superstrings on AdS(5)× S**5 Commun. Math. Phys. 263 659 (Preprint hep-th/0502226)
50. Beisert N, Kazakov V A, Sakai K and Zarembo K 2005 Complete spectrum of long operators in N ≤ 4 SYM at one loop J. High Energy Phys. JHEP07(2005)030 (Preprint hep-th/0503200)
51. Beisert N, Dippel V and Staudacher M 2004 A novel long range spin chain and planar N ≤ 4 super Yang-Mills J. High Energy Phys. JHEP07(2004)075 (Preprint hep-th/0405001)
52. Rej A, Serban D and Staudacher M 2005 Planar N ≤ 4 gauge theory and the Hubbard model Preprint hep-th/0512077
53. Arutyunov G, Frolov S and Staudacher M 2004 Bethe ansatz for quantum strings J. High Energy Phys. JHEP10(2004)016 (Preprint hep-th/0406256)
54. Gromov N and Kazakov V 2006 Asymptotic Bethe ansatz from string sigma model on S**3 × R Preprint hep-th/0605026
55. Kruczenski M 2004 Spin chains and string theory Phys. Rev. Lett. 93 161602 (Preprint hep-th/0311203)
56. Kruczenski M, Ryzhov A V and Tseytlin A A 2004 Large spin limit of AdS(5)× S**5 string theory and low energy expansion of ferromagnetic spin chains Nucl. Phys. B 692 3 (Preprint hep-th/0403120)
57. Hernandez R and Lopez E 2004 The SU(3) spin chain sigma model and string theory J. High Energy Phys. JHEP04(2004)052 (Preprint hep-th/0403139)
58. Stefanski B J and Tseytlin A A 2004 Large spin limits of AdS/CFT and generalized Landau-Lifshitz equations J. High Energy Phys. JHEP05(2004)042 (Preprint hep-th/0404133)
59. Ryzhov A V and Tseytlin A A 2004 Towards the exact dilatation operator of N ≤ 4 super Yang-Mills theory Nucl. Phys. B 698 132 (Preprint hep-th/0404215)
60. Kruczenski M and Tseytlin A A 2004 Semiclassical relativistic strings in S**5 and long coherent operators in N ≤ 4 SYM theory J. High Energy Phys. JHEP09(2004)038 (Preprint hep-th/0406189)
61. Callan C G, Heckman J, McLoughlin T and Swanson I J 2004 Lattice super Yang-Mills: a virial approach to operator dimensions Nucl. Phys. B 701 180 (Preprint hep-th/0407096)
62. Bellucci S, Casteill P Y, Morales J F and Sochichiu C 2005 SL(2) spin chain and spinning strings on AdS(5)× S**5 Nucl. Phys. B 707 303 (Preprint hep-th/0409086)
63. Hernandez R and Lopez E 2004 Spin chain sigma models with fermions J. High Energy Phys. JHEP11(2004)079 (Preprint hep-th/0410022)
64. Bellucci S, Casteill P Y and Morales J F 2005 Superstring sigma models from spin chains: the SU(1, 1|1) case Nucl. Phys. B 729 163 (Preprint hep-th/0503159)
65. Minahan J A, Tirziu A and Tseytlin A A 2006 1/J corrections to semiclassical AdS/CFT states from quantum Nucl. Phys. B 735 127 (Preprint hep-th/0509071)
66. Minahan J A, Tirziu A and Tseytlin A A 2005 1/J**2 corrections to BMN energies from the quantum long range Landau-Lifshitz model J. High Energy Phys. JHEP11(2005)031 (Preprint hep-th/0510080)
67. Bellucci S and Casteill P Y 2006 Sigma model from SU(1, 1|2) spin chain Nucl. Phys. B 741 297 (Preprint hep-th/0602007)
68. Roiban R, Tirziu A and Tseytlin A A 2006 Asymptotic Bethe ansatz S-matrix and Landau-Lifshitz type effective 2-d actions Preprint hep-th/0604199
69. Frolov S and Tseytlin A A 2003 Quantizing three-spin string solution in AdS(5)× S**5 J. High Energy Phys. JHEP07(2003)016 (Preprint hep-th/0306130)
70. Frolov S A, Park I Y and Tseytlin A A 2005 On one-loop correction to energy of spinning strings in S(5) Phys. Rev. D 71 026006 (Preprint hep-th/0408187)
71. Park I Y, Tirziu A and Tseytlin A A 2005 Spinning strings in AdS(5)× S**5: one-loop correction to energy in SL(2) sector J. High Energy Phys. JHEP03(2005)013 (Preprint hep-th/0501203)
72. Schafer-Nameki S, Zamaklar M and Zarembo K 2005 Quantum corrections to spinning strings in AdS(5)× S**5 and Bethe ansatz: a comparative study J. High Energy Phys. JHEP09(2005)051 (Preprint hep-th/0507189)
73. Beisert N and Tseytlin A A 2005 On quantum corrections to spinning strings and Bethe equations Phys. Lett. B 629 102 (Preprint hep-th/0509084)
74. Schafer-Nameki S and Zamaklar M 2005 Stringy sums and corrections to the quantum string Bethe ansatz J. High Energy Phys. JHEP10(2005)044 (Preprint hep-th/0509096)
75. Schafer-Nameki S 2006 Exact expressions for quantum corrections to spinning strings Preprint hep-th/0602214
76. Hernandez R and Lopez E 2006 Quantum corrections to the string Bethe ansatz J. High Energy Phys. JHEP07(2006)004 (Preprint hep-th/0603204)
77. Freyhult L and Kristjansen C 2006 A universality test of the quantum string Bethe ansatz Phys. Lett. B 638 258 (Preprint hep-th/0604069)
78. Staudacher M 2005 The factorized S-matrix of CFT/AdS J. High Energy Phys. JHEP05(2005)054 (Preprint hep-th/0412188)
79. Beisert N and Staudacher M 2005 Long-range PSU(2, 2|4) Bethe ansatz for gauge theory and strings Nucl. Phys. B 727 1 (Preprint hep-th/0504190)
80. Beisert N 2005 The su(2-2) dynamic S-matrix Preprint hep-th/0511082
81. Janik R A 2006 The AdS(5)× S**5 superstring worldsheet S-matrix and crossing symmetry Phys. Rev. D 73 086006 (Preprint hep-th/0603038)
82. Arutyunov G and Frolov S 2006 On AdS(5)× S**5 string S-matrix Phys. Lett. B 639 378 (Preprint hep-th/0604043)
83. Beisert N 2006 On the scattering phase for AdS(5)× S**5 strings Preprint hep-th/0606214
84. Mann N and Polchinski J 2005 Bethe ansatz for a quantum supercoset sigma model Phys. Rev. D 72 086002 (Preprint hep-th/0508232)
85. Gromov N, Kazakov V, Sakai K and Vieira P 2006 Strings as multi-particle states of quantum sigma-models Preprint hep-th/0603043
86. Klsose T and Zarembo K 2006 Bethe ansatz in stringy sigma models Preprint hep-th/0603039
87. Tseytlin A A 2003 Spinning strings and AdS/CFT duality Preprint hep-th/0311139
88. Zarembo K 2004 Semiclassical Bethe ansatz and AdS/CFT C. R. Phys. 5 1081 (Fortsch. Phys. 53 647 (2005)) (Preprint hep-th/0411191)
89. Plefka J 2005 Spinning strings and integrable spin chains in the AdS/CFT correspondence Preprint hep-th/0507136
90. Faddeev L D 1996 How algebraic Bethe ansatz works for integrable model Preprint hep-th/9605187