Long-range gl(n) integrable spin chains and plane-wave matrix theory

Journal of Statistical Mechanics: Theory and Experiment

Volumn , Issue 7, 2006, Pages

  Beisert, N ^a   Klose, T ^b,c  

^a PRINCETON UNIVERSITY   (United States)

^b UPPSALA UNIVERSITY   (Sweden)

^c ALBERT EINSTEIN INSTITUT   (Germany)

Author keywords

Integrable spin chains (vertex models); Quantum integrability (Bethe ansatz)

Indexed keywords

EID: 37649028918     PISSN: 17425468     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2006/07/P07006     Document Type: Article

References (58)

1. Minahan J A and Zarembo K 2003 The Bethe-ansatz for super Yang-Mills J. High Energy Phys. JHEP03(2003)013 [hep-th/0212208]
2. Beisert N, Kristjansen C and Staudacher M 2003 The dilatation operator of conformal super Yang-Mills theory Nucl. Phys. B 664 131 [hep-th/0303060]
3. Beisert N 2004 The su(2/3) dynamic spin chain Nucl. Phys. B 682 487 [hep-th/0310252]
4. 2 exchange Phys. Rev. Lett. 60 635
5. Shastry B S 1988 Exact solution of an S ≤ 1/2 Heisenberg antiferromagnetic chain with long ranged interactions Phys. Rev. Lett. 60 639
6. Inozemtsev V I 1990 On the connection between the one-dimensional s ≤ 1/2 Heisenberg chain and Haldane Shastry model J. Stat. Phys. 59 1143
7. Inozemtsev V I 2003 Integrable Heisenberg-van Vleck chains with variable range exchange Phys. Part. Nucl. 34 166 [hep-th/0201001]
8. Beisert N and Staudacher M 2003 The SYM integrable super spin chain Nucl. Phys. B 670 439 [hep-th/0307042]
9. Serban D and Staudacher M 2004 Planar gauge theory and the Inozemtsev long range spin chain J. High Energy Phys. JHEP06(2004)001 [hep-th/0401057]
10. Beisert N, Dippel V and Staudacher M 2004 A novel long range spin chain and planar super Yang-Mills J. High Energy Phys. JHEP07(2004)075 [hep-th/0405001]
11. Staudacher M 2005 The factorized S-matrix of CFT/AdS J. High Energy Phys. JHEP05(2005)054 [hep-th/0412188]
12. Beisert N and Staudacher M 2005 Long-range PSU(2,2/4) Bethe ansaetze for gauge theory and strings Nucl. Phys. B 727 1 [hep-th/0504190]
13. 5 Phys. Lett. B 543 81 [hep-th/0206103]
14. 5 superstring Phys. Rev. D 69 046002 [hep-th/0305116]
15. 5 and integrable systems Nucl. Phys. B 671 3 [hep-th/0307191]
16. 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 [hep-th/0402207]
17. Arutyunov G, Frolov S and Staudacher M 2004 Bethe ansatz for quantum strings J. High Energy Phys. JHEP10(2004)016 [hep-th/0406256]
18. 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 [hep-th/0204051]
19. 5: beyond the pp-wave Nucl. Phys. B 673 3 [hep-th/0307032]
20. McLoughlin T and Swanson I 2004 N-impurity superstring spectra near the pp-wave limit Nucl. Phys. B 702 86 [hep-th/0407240]
21. 5 Phys. Rev. D 71 026006 [hep-th/0408187]
22. 5: one-loop correction to energy in SL(2) sector J. High Energy Phys. JHEP03(2005)013 [hep-th/0501203]
23. Schäfer-Nameki S and Zamaklar M 2005 Stringy sums and corrections to the quantum string Bethe ansatz J. High Energy Phys. JHEP10(2005)044 [hep-th/0509096]
24. Beisert N and Tseytlin A A 2005 On quantum corrections to spinning strings and Bethe equations Phys. Lett. B 629 102 [hep-th/0509084]
25. Beisert N, Tseytlin A A and Zarembo K 2005 Matching quantum strings to quantum spins: one-loop vs finite-size corrections Nucl. Phys. B 715 190 [hep-th/0502173]
26. Hernández R, López E, Periáñez A and Sierra G 2005 Finite size effects in ferromagnetic spin chains and quantum corrections to classical strings J. High Energy Phys. JHEP06(2005)011 [hep-th/0502188]
27. 5 and Bethe ansatz: a comparative study J. High Energy Phys. JHEP09(2005)051 [hep-th/0507189]
28. Beisert N 2005 Spin chain for quantum strings Fortschr. Phys. 53 852 [hep-th/0409054]
29. Lee C W H and Rajeev S G 1998 Symmetry algebras of large-N matrix models for open strings Nucl. Phys. B 529 656 [hep-th/9712090]
30. Lee C W H and Rajeev S G 1998 Symmetries of large N(c) matrix models for closed strings Phys. Rev. Lett. 80 2285 [hep-th/9711052]
31. Berenstein D, Maldacena J M and Nastase H 2002 Strings in flat space and pp waves from super Yang Mills J. High Energy Phys. JHEP04(2002)013 [hep-th/0202021]
32. Dasgupta K, Sheikh-Jabbari M M and Van Raamsdonk M 2002 Matrix perturbation theory for M-theory on a PP-wave J. High Energy Phys. JHEP05(2002)056 [hep-th/0205185]
33. 3 Nucl. Phys. B 671 359 [hep-th/0306054]
34. Klose T and Plefka J 2004 On the integrability of large N plane-wave matrix theory Nucl. Phys. B 679 127 [hep-th/0310232]
35. Fischbacher T, Klose T and Plefka J 2005 Planar plane-wave matrix theory at the four loop order: integrability without BMN scaling J. High Energy Phys. JHEP02(2005)039 [hep-th/0412331]
36. Beisert N 2005 The dilatation operator of super Yang-Mills theory and integrability Phys. Rep. 405 1 [hep-th/0407277]
37. Beisert N 2004 Higher-loop integrability in gauge theory C. R. Phys. 5 1039 [hep-th/0409147]
38. Zarembo K 2004 Semiclassical Bethe ansatz and AdS/CFT C. R. Phys. 5 1081 [hep-th/0411191]
39. Klose T 2005 Plane wave matrix theory: gauge theoretical origin and planar integrability PhD Thesis
40. Tseytlin A A 2005 Spinning strings and AdS/CFT duality From Fields to Stings: Circumnavigating Theoretical Physics ed M Shifman, A Vainshtein and J Wheater (Singapore: World Scientific) [hep-th/0311139]
41. Plefka J 2005 Spinning strings and integrable spin chains in the AdS/CFT correspondence Living Rev. Rel. 8 9 [hep-th/0507136]
42. Bethe H 1931 On the theory of metals. 1. Eigenvalues and eigenfunctions for the linear atomic chain Z. Phys. 71 205
43. Sutherland B 1978 A brief history of the quantum soliton with new results on the quantization of the Toda lattice Rocky Mountain J. Math. 8 413
44. Dymarsky A, Klebanov I R and Roiban R 2005 Perturbative search for fixed lines in large N gauge theories J. High Energy Phys. JHEP08(2005)011 [hep-th/0505099]
45. Dymarsky A, Klebanov I R and Roiban R 2005 Perturbative gauge theory and closed string tachyons J. High Energy Phys. JHEP11(2005)038 [hep-th/0509132]
46. Freedman D Z and Gürsoy U 2005 Comments on the beta-deformed SYM theory J. High Energy Phys. JHEP11(2005)042 [hep-th/0506128]
47. Penati S, Santambrogio A and Zanon D 2005 Two-point correlators in the beta-deformed SYM at the next-to-leading order J. High Energy Phys. JHEP10(2005)023 [hep-th/0506150]
48. Rossi G C, Sokatchev E and Stanev Y S 2005 New results in the deformed SYM theory Nucl. Phys. B 729 581 [hep-th/0507113]
49. Grabowski M P and Mathieu P 1995 Integrability test for spin chains J. Phys. A: Math. Gen. 28 4777 [hep-th/9412039]
50. Bernard D 1993 An introduction to Yangian symmetries Int. J. Mod. Phys. B 7 3517 [hep-th/9211133]
51. 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 [hep-th/0308089]
52. Agarwal A and Rajeev S G 2005 Yangian symmetries of matrix models and spin chains: the dilatation operator of SYM Int. J. Mod. Phys. A 20 5453 [hep-th/0409180]
53. Ogievetsky E and Wiegmann P 1986 Factorized S matrix and the Bethe ansatz for simple Lie groups Phys. Lett. B 168 360
54. Eden B, Jarczak C and Sokatchev E 2005 A three-loop test of the dilatation operator in SYM Nucl. Phys. B 712 157 [hep-th/0409009]
55. Klose T 2005 On the breakdown of perturbative integrability in large N matrix models J. High Energy Phys. JHEP10(2005)083 [hep-th/0507217]
56. Beisert N 2004 The complete one-loop dilatation operator of super Yang-Mills theory Nucl. Phys. B 676 3 [hep-th/0307015]
57. Dasgupta K, Sheikh-Jabbari M M and Van Raamsdonk M 2002 Protected multiplets of M-theory on a plane wave J. High Energy Phys. JHEP09(2002)021 [hep-th/0207050]
58. Lin H and Maldacena J 2005 Fivebranes from gauge theory Preprint hep-th/0509235