The algebraic curve of classical superstrings on AdS 5 × S 5

Communications in Mathematical Physics

Volumn 263, Issue 3, 2006, Pages 659-710

  Beisert, N ^a   Kazakov, V A ^b,d   Sakai, K ^b   Zarembo, K ^c,e  

^a PRINCETON UNIVERSITY   (United States)

^b LABORATOIRE DE PHYSIQUE STATISTIQUE   (France)

^c UPPSALA UNIVERSITY   (Sweden)

^d INSTITUT UNIVERSITAIRE DE FRANCE   (France)

^e INSTITUTE FOR THEORETICAL AND EXPERIMENTAL PHYSICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33645323759     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-006-1529-4     Document Type: Article

References (81)

1. Maldacena, J.M.: The large N limit of superconformal field theories and supergravity. Adv. Theor. Math. Phys. 2, 231 (1998)
2. Gubser, S.S., Klebanov, I.R., Polyakov, A.M.: Gauge theory correlators from non-critical string theory. Phys. Lett. B428, 105 (1998)
3. Witten, E.: Anti-de Sitter space and holography. Adv. Theor. Math. Phys. 2, 253 (1998)
4. 5 background. Nucl. Phys. B533, 109 (1998)
5. Blau, M., Figueroa-O'Farrill, J., Hull, C., Papadopoulos, G.: A new maximally supersymmetric background of IIB superstring theory. JHEP 0201, 047 (2002)
6. Blau, M., Figueroa-O'Farrill, J., Hull, C., Papadopoulos, G.: Penrose limits and maximal super-symmetry Class. Quant. Grav. 19, L87 (2002)
7. Berenstein, D., Maldacena, J.M., Nastase, H.: Strings in flat space and pp waves from N = 4 Super Yang Mills JHEP 0204, 013 (2002)
8. Metsaev, R.R.: Type IIB Green-Schwarz superstring in plane wave Ramond-Ramond background. Nucl. Phys. B625, 70 (2002)
9. Metsaev, R.R., Tseytlin, A.A.: Exactly solvable model of superstring in plane wave Ramond-Ramond background. Phys. Rev. D65, 126004 (2002)
10. 5: Beyond the pp-wave. Nucl. Phys. B673, 3 (2003)
11. Parnachev, A., Ryzhov, A.V.: Strings in the near plane wave background and AdS/CFT. JHEP 0210, 066 (2002)
12. Callan, Jr., C.G., McLoughlin, T., Swanson, I.: Holography beyond the Penrose limit. Nucl. Phys. B694, 115 (2004)
13. Callan, Jr. C.G., McLoughlin, T., Swanson, I.: Higher impurity AdS/CFT correspondence in the near-BMN limit. Nucl. Phys. B700, 271 (2004)
14. McLoughlin, T., Swanson, I.: N-impurity superstring spectra near the pp-wave limit. Nucl. Phys. B702, 86 (2004)
15. Gubser, S.S., Klebanov, I.R., Polyakov, A.M.: A semi-classical limit of the gauge/string correspondence. Nucl. Phys. B636, 99 (2002)
16. 5 × S5. JHEP 0206, 007 (2002)
17. 5. JHEP 0206, 038 (2002)
18. 5. Nucl. Phys. B648, 203 (2003)
19. 5 and beyond. Int. J. Mod. Phys. A18, 981 (2003)
20. 5. Nucl. Phys. B668, 77 (2003)
21. Beisert, N., Minahan, J.A., Staudacher, M., Zarembo, K.: Stringing Spins and Spinning Strings. JHEP 0309, 010 (2003)
22. Beisert, N., Frolov, S., Staudacher, M., Tseytlin, A.A.: Precision Spectroscopy of AdS/CFT. JHEP 0310, 037 (2003)
23. Serban, D., Staudacher, M.: Planar N = 4 gauge theory and the Inozemtsev long range spin chain. JHEP 0406, 001 (2004)
24. Tseytlin, A.A.: Spinning strings and AdS/CFT duality. In: M. Shifman, A. Vainshtein J. Wheater (eds.) From Fields to Stings: Circumnavigating Theoretical Physics, Ian Kogan Memorial Volume, Singapore: World Scientific, 2005
25. 5 and scalar operators in M = 4 SYM theory. Comptes Rendus Physique 5, 1049 (2004)
26. Beisert, N.: The Dilatation Operator of N = 4 Super Yang-Mills Theory and Integrability. Phys. Rept. 405, 1 (2005)
27. Beisert, N.: Higher-loop integrability in N = 4 gauge theory. Comptes Rendus Physique 5, 1039 (2004)
28. Zarembo, K.: Semiclassical Bethe ansatz and AdS/CFT. Comptes Rendus Physique 5, 1081 (2004)
29. Kazakov, V.A., Marshakov, A., Minahan, J.A., Zarembo, K.: Classical/quantum integrability in AdS/CFT. JHEP 0405, 024 (2004)
30. 5 and integrable systems. Nucl. Phys. B671, 3 (2003)
31. 5: New integrable system relations. Phys. Rev. D69, 086009 (2004)
32. Zakharov, V.E., Mikhailov, A.V.: Relativistically invariant two-dimensional models in field theory integrable by the inverse problem technique. Sov. Phys. JETP 47, 1017 (1978), in Russian
33. Pohlmeyer, K.: Integrable Hamiltonian systems and interactions through quadratic constraints. Commun. Math. Phys. 46, 207 (1976)
34. Lüscher, M., Pohlmeyer, K.: Scattering of massless lumps and nonlocal charges in the two-dimensional classical nonlinear sigma model. Nucl. Phys. B137, 46 (1978)
35. Brezin, E., Itzykson, C., Zinn- Justin, J., Zuber, J.B.: Remarks aboutthe existence of nonlocal charges in two-dimensional models. Phys. Lett. B82, 442 (1979)
36. Eichenherr, H., Forger, M.: Higher local conservation laws for nonlinear sigma models on symmetric spaces. Commun. Math. Phys. 82, 227 (1981)
37. Minahan, J.A., Zarembo, K.: The Bethe-ansatz for N = 4 super Yang-Mills. JHEP 0303, 013 (2003)
38. Beisert, N., Staudacher, M.: The N = 4 SYM Integrable Super Spin Chain. Nucl. Phys. B670, 439 (2003)
39. Beisert, N., Kristjansen, C., Staudacher, M.: The dilatation operator of N = 4 conformal super Yang-Mills theory. Nucl. Phys. B664, 131 (2003)
40. Beisert, N.: The su(2/3) dynamic spin chain. Nucl. Phys. B682, 487 (2004)
41. Staudacher, M.: The factorized S-matrix of CFT/AdS. JHEP 0505, 054 (2005)
42. Beisert, N., Dippel, V., Staudacher, M.: A Novel Long Range Spin Chain and Planar N = 4 Super Yang-Mills. JHEP 0407, 075 (2004)
43. Sutherland, B.: Low-Lying Eigenstates of the One-Dimensional Heisenberg Ferromagnet for any Magnetization and Momentum. Phys. Rev. Lett. 74, 816 (1995)
44. Kruczenski, M.: Spin chains and string theory. Phys. Rev. Lett. 93, 161602 (2004)
45. 5 string theory and low energy expansion of ferromagnetic spin chains. Nucl. Phys. B692, 3 (2004)
46. Kazakov, V.A., Zarembo, K.: Classical/quantum integrability in non-compact sector of AdS/CFT. JHEP 0410, 060 (2004)
47. Beisert, N., Kazakov, V.A., Sakai, K.: Algebraic curve for the SO(6) sector of AdS/CFT. http://ar-Xiv.org/list/hep-th/0410253, 2004, to appear in Commun. Math. Phys.
48. Schäfer-Nameki, S.: The algebraic curve of 1-loop planar N = 4 SYM. Nucl. Phys. B714, 3 (2005)
49. 5. JHEP 0502, 059 (2005)
50. Mikhailov, A.: Supersymmetric null-surf aces. JHEP 0409, 068 (2004)
51. Hernandez, R., López, E.: Spin chain sigma models with fermions. JHEP 0411, 079 (2004)
52. 5 superstring. Phys. Rev. D69, 046002 (2004)
53. Beisert, N.: The Complete One-Loop Dilatation Operator of N = 4 Super Yang-Mills Theory. Nucl. Phys. B676, 3 (2004)
54. Beisert, N., Kazakov, V. A., Sakai, K., Zarembo, K.: Complete Spectrum of Long Operators in N = 4 SYM at One Loop. JHEP 0507, 030 (2005)
55. 5. Int. J. Mod. Phys. A19, 4715 (2004)
56. 5 superstring. JHEP 0412, 055 (2004)
57. Kallosh, R., Rahmfeld, J., Rajaraman, A.: Near horizon superspace. JHEP 9809, 002 (1998)
58. 2 as a coset supermanifold. Nucl. Phys. B567, 61 (2000)
59. 5 supertwistor space. JHEP 0011, 024 (2000)
60. Berkovits, N.: BRST cohomology and nonlocal conserved charges. JHEP 0502, 060 (2005)
61. 5 background. JHEP 0503, 041 (2005)
62. Mikhailov, A.: Notes on fast moving strings, hep-th/0409040.
63. Mikhailov, A.: Plane wave limit of local conserved charges. JHEP 0510, 093 (2005)
64. Berkovits, N., Vafa, C., Witten, E.: Conformal field theory of AdS background with Ramond-Ramond flux. JHEP 9903, 018 (1999)
65. 3 background with Ramond-Ramond flux. JHEP 9911, 003 (1999)
66. 3 Ramond-Ramond background in light-cone gauge. J. Math. Phys. 42, 2987 (2001)
67. Arutyunov, G., Staudacher, M.: Matching Higher Conserved Charges for Strings and Spins. JHEP 0403, 004 (2004)
68. Arutyunov, G., Staudacher, M.: Two-loop commuting charges and the string/gauge duality. In: "Lie Theory and its Applications in Physics V", Proceedings of the Fifth International Workshop, Varna, Bulgaria, 16-22 June 2003, H.-D. Doebner, V.K. Dobrev, (ed.) Singapore: World Scientific, 2004
69. Arutyunov, G., Frolov, S., Staudacher, M.: Bethe ansatz for quantum strings. JHEP 0410, 016 (2004)
70. Beisert, N.: Spin chain for quantum strings. Fortsch. Phys. 53, 852 (2005)
71. Swanson, I.: Quantum string integrability and AdS/CFT. Nucl. Phys. B709, 443 (2005)
72. Beisert, N., Tseytlin, A.A., Zarembo, K.: Matching quantum strings to quantum spins: one-loop vs. finite-size corrections. Nucl. Phys. B715, 190 (2005)
73. Hernández, R., López, E., Periáñez, A., Sierra, G.: Finite size effects in ferromagnetic spin chains and quantum corrections to classical strings. JHEP 0506, 011 (2005)
74. Polyakov, A.M., Wiegmann, P.B.: Theory of nonabelian Goldstone bosons in two dimensions. Phys. Lett. B131, 121 (1983)
75. Polyakov, A.M., Wiegmann, P.B.: Goldstone fields in two-dimensions with multivalued actions. Phys. Lett. 8141, 223 (1984)
76. Faddeev, L.D., Reshetikhin, N.Y.: Integrability of the principal chiral field model in (1 + 1)-dimension. Ann. Phys. 167, 227 (1986)
77. Ogievetsky, E., Wiegmann, P., Reshetikhin, N.: The principal chiral field in two-dimensions on classical Lie algebras: The Bethe ansatz solution and factorized theory of scattering. Nucl. Phys. B280, 45 (1987)
78. Novikov, S., Manakov, S.V., Pitaevsky, L.P., Zakharov, V.E.: "Theory of Solitons. The Inverse Scattering Method". Contemporary Soviet Mathematics. (1984) New York: Consultants Bureau, 276p
79. Its, A.R., Matveev, V.B.: Schrödinger operators with finite-gap spectrum and N-soliton solutions of the Korteweg-de Vries equation. Theor. Math. Phys. 23, 343 (1975)
80. Dubrovin, B.A., Novikov, M.V.B., Novikov, S.P.: Non-linear equations of Korteweg-de Vries type, finite zone linear operators, and Abelian varieties. Russ. Math. Surv 31, 59 (1976)
81. Krichever, I.M.: Elliptic solutions of KP equations and integrable systems of particles. Funk. Anal. App. 14, 282 (1980)