Analytical Bethe ansatz for closed and open gl(\cM|\cN)super-spin chains in arbitrary representations and for any Dynkin diagram

Journal of High Energy Physics

Volumn 2007, Issue 9, 2007, Pages

  Ragoucy, Eric ^a   Satta, Giovanni ^a,b  

^a LABORATOIRE DE PHYSIQUE DES PARTICULES   (France)

^b ROMA TRE UNIVERSITY   (Italy)

Author keywords

Bethe Ansatz; Integrable gierarchies; Lattice integrable models

Indexed keywords

EID: 34948883977     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2007/09/001     Document Type: Article

References (34)

1. R.J. Baxter, Partition function of the eight-vertex lattice model 1972 Ann. Phys. (NY) 70 193
2. R.J. Baxter, Asymptotically degenerate maximum eigenvalues of the eight- vertex model transfer matrix and interfacial tension 1973 J. Statist. Phys. 8 25
3. R.J. Baxter, Exactly solved models in statistical mechanics (Academic Press) (1982)
4. I.V. Cherednik, Factorizing particles on a half line and root systems 1984 Theor. Math. Phys. 61 977
5. E.K. Sklyanin, Boundary conditions for integrable quantum systems 1988 J. Phys. A: Math. Gen. 21 2375
6. P.P. Kulish and E.K. Sklyanin, Algebraic structures related to the reflection equations 1992 J. Phys. A: Math. Gen. 25 5963 [hep-th/9209054]
7. P.P. Kulish and R. Sasaki, Covariance properties of reflection equation algebras 1993 Prog. Theor. Phys. 89 741 [hep-th/9212007]
8. J. Donin, P. Kulish and A. Mudrov, On universal solution to reflection equation, 2003 Lett. Math. Phys. 63 179 [math.QA/0210242]
9. A. Arnaudon, N. Crampé, A. Doikou, L. Frappat and. Ragoucy, Analytical Bethe ansatz for closed and open gl(n)-spin chains in any representation 2005 J. Stat. Mech. P02007 [math-ph/0411021]
10. q(gl(N)) closed and open spin chains in any representation, 2006 Ann. H. Poincaré 7 1217 [math.QA/0512037]
11. 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]
12. N. Beisert and M. Staudacher, The N ≤ 4 SYM integrable super spin chain 2003 Nucl. Phys. B 670 439 [hep-th/0307042]
13. N. Beisert, The SU(2|3) dynamic spin chain, 2004 Nucl. Phys. B 682 487 [hep-th/0310252]
14. 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]
15. P. Kulish, Integrable graded magnets, 1986 J. Sov. Math. 35 2648
16. H. Saleur, The continuum limit of sl(N/K) integrable super spin chains 2000 Nucl. Phys. B 578 552 [solv-int/9905007]
17. M.J. Martins, Integrable mixed vertex models from braid-monoid algebra [solv-int/9903006]
18. Z. Tsuboi, Analytic Bethe ansatz and functional equations associated with any simple root systems of the lie superalgebra sl(r+1|s+1) 1998 Physica A 252 565
19. Z. Tsuboi, Analytic Bethe ansatz related to a one-parameter family of finite-dimensional representations of the lie superalgebra sl(r+1|s+1) 1998 J. Phys. A: Math. Gen. 31 5485
20. V. Kazakov, A. Sorin and A. Zabrodin, Supersymmetric Bethe ansatz and baxter equations from discrete hirota dynamics [hep-th/0703147]
21. A. Gonzlez-Ruiz, Integrable open boundary conditions for the supersymmetric t-J model. the quantum group invariant case 1994 Nucl. Phys. B 424 468 [hep-th/9401118]
22. F.H.L. Essler, The supersymmetric t-J model with a boundary 1996 J. Phys. A: Math. Gen. 29 6183 [cond-mat/9605180]
23. F.H.L. Essler and V.E. Korepin, Higher conservation laws and algebraic Bethe ansatze for the supersymmetric t-J model 1992 Phys. Rev. B 46 9147
24. F.H.L. Essler, A new solution of the supersymmetric t-J model by means of the quantum inverse scattering method [hep-th/9207007]
25. q(n|m) model, 1996 Nucl. Phys. B 462 167 [cond-mat/9603022]
26. L. Frappat, A. Sciarino and P. Sorba, Dictionary on Lie algebras and superalgebras San Diego, (Academic Press) (2000)
27. L. Faddeev, N. Reshetikhin and L. Takhtajan, Quantization of Lie groups and Lie algebras, 1990 Leningrad Math. J. 1 193
28. R.-B. Zhang, The gl(M|N) super Yangian and its finite dimensional representations 1996 Lett. Math. Phys. 37 419 [q-alg/9507029]
29. M. Nazarov, Quantum Berezinian and the classical Capelli Identity 1991 Lett. Math. Phys. 21 123
30. A. Molev, Yangians and their applications in Handbook of Algebra Vol. 3, (M. Hazewinkel, Ed.), Elsevier (2003), [math.QA/0211288]
31. A. Molev and E. Ragoucy, Representation of reflection algebras 2002 Rev. Math. Phys. 14 317 [math.QA/0107213]
32. D. Arnaudon et al., General boundary conditions for the sl(N) and sl(M|N) open spin chains 2004 J. Stat. Mech. P08005 [math-ph/0406021]
33. q(sl(N|M)) vertex model with mixed representations 2006 Nucl. Phys. B 738 391 [nlin/0512035]
34. H.J. de Vega and F. Woynarovich, New integrable quantum chains combining different kinds of spins 1992 J. Phys. A: Math. Gen. 25 4499