Yangian symmetry of long-range gl (N) integrable spin chains

Journal of Statistical Mechanics: Theory and Experiment

Volumn 2008, Issue 3, 2008, Pages

  Beisert, Niklas ^a   Erkal, Denis ^b  

^a ALBERT EINSTEIN INSTITUT   (Germany)

^b UNIVERSITY OF CHICAGO   (United States)

Author keywords

Algebraic structures of integrable models; Integrable spin chains (vertex models); Quantum integrability (Bethe ansatz); Symmetries of integrable models

Indexed keywords

EID: 43149125447     PISSN: 17425468     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2008/03/P03001     Document Type: Article

References (35)

1. Drinfeld V G 1985 Hopf algebras and the quantum Yang-Baxter equation Sov. Math. Dokl. 32 254
2. Drinfeld V G 1988 Quantum groups J. Sov. Math. 41 898
3. Bernard D 1993 An introduction to Yangian symmetries Int. J. Mod. Phys. B 7 3517 [hep-th/9211133]
4. MacKay N J 2005 Introduction to Yangian symmetry in integrable field theory Int. J. Mod. Phys. A 20 7189 [hep-th/0409183]
5. 2 exchange Phys. Rev. Lett. 60 635
6. Shastry B S 1988 Exact solution of an S = 1/2 Heisenberg antiferromagnetic chain with long ranged interactions Phys. Rev. Lett. 60 639
7. 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]
8. Beisert N 2005 Spin chain for quantum strings Fortschr. Phys. 53 852 [hep-th/0409054]
9. Beisert N and Klose T 2006 Long-range GL(n) integrable spin chains and plane-wave matrix theory J. Stat. Mech. P07006 [hep-th/0510124]
10. Beisert N, Eden B and Staudacher M 2007 Transcendentality and crossing J. Stat. Mech. P01021 [hep-th/0610251]
11. Maldacena J M 1998 The large N limit of superconformal field theories and supergravity Adv. Theor. Math. Phys. 2 231 [hep-th/9711200]
12. Minahan J A and Zarembo K 2003 The Bethe-ansatz for super Yang-Mills J. High Energy Phys. JHEP03(2003)013 [hep-th/0212208]
13. 5 superstring Phys. Rev. D 69 046002 [hep-th/0305116]
14. Beisert N and Staudacher M 2003 The SYM integrable super spin chain Nucl. Phys. B 670 439 [hep-th/0307042]
15. Beisert N 2004 The dilatation operator of N = 4 super Yang-Mills theory and integrability Phys. Rep. 405 1 [hep-th/0407277]
16. Plefka J 2005 Spinning strings and integrable spin chains in the AdS/CFT correspondence Living. Rev. Relativity 8 9 [hep-th/0507136]
17. 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 [hep-th/0202021]
18. Klose T and Plefka J 2004 On the integrability of large N plane-wave matrix theory Nucl. Phys. B 679 127 [hep-th/0310232]
19. 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]
20. 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
21. Inozemtsev V I 2003 Integrable Heisenberg-van Vleck chains with variable range exchange Phys. Part. Nucl. 34 166 [hep-th/0201001]
22. 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]
23. Rej A, Serban D and Staudacher M 2006 Planar gauge theory and the Hubbard model J. High Energy Phys. JHEP03(2006)018 [hep-th/0512077]
24. Staudacher M 2005 The factorized S-matrix of CFT/AdS J. High Energy Phys. JHEP05(2005)054 [hep-th/0412188]
25. 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]
26. Arutyunov G, Frolov S and Staudacher M 2004 Bethe ansatz for quantum strings J. High Energy Phys. JHEP10(2004)016 [hep-th/0406256]
27. Beisert N, McLoughlin T and Roiban R 2007 The four-loop dressing phase of SYM Phys. Rev. D 76 046002 [0705.0321]
28. 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]
29. Dolan L, Nappi C R and Witten E 2004 Yangian symmetry in D = 4 superconformal Yang-Mills theory Quantum Theory and Symmetries ed P C Argyres et al (Singapore: World Scientific) [hep-th/0401243]
30. 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]
31. Zwiebel B I 2007 Yangian symmetry at two-loops for the su(2/1) sector of SYM J. Phys. A: Math. Theor. 40 1141 [hep-th/0610283]
32. 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]
33. Beisert N 2005 The SU(2/2) dynamic S-matrix Preprint hep-th/0511082
34. Grabowski M P and Mathieu P 1995 Integrability test for spin chains J. Phys. A: Math. Gen. 28 4777 [hep-th/9412039]
35. Beisert N 2004 The SU(2/3) dynamic spin chain Nucl. Phys. B 682 487 [hep-th/0310252]