String Hypothesis for gl(n{pipe}m) Spin Chains: A Particle/Hole Democracy

Letters in Mathematical Physics

Volumn 102, Issue 1, 2012, Pages 1-29

  Volin, Dmytro ^a,b  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b BOGOLYUBOV INSTITUTE FOR THEORETICAL PHYSICS   (Ukraine)

Author keywords

AdS CFT; Bethe Ansatz; integrability; representation theory

Indexed keywords

EID: 84865817966     PISSN: 03779017     EISSN: 15730530     Source Type: Journal    
DOI: 10.1007/s11005-012-0570-9     Document Type: Article

References (54)

1. Zamolodchikov A. B.: On the thermodynamic Bethe ansatz equations for reflectionless ADE scattering theories. Phys. Lett. B253, 391-394 (1991).
2. Gromov, N., Kazakov, V., Vieira, P.: Finite volume spectrum of 2D field theories from hirota dynamics. JHEP 2009(12), 060 (2008). http://xxx. lanl. gov/abs/0812. 5091.
3. Gromov, N., Kazakov, V., Vieira, P.: Exact spectrum of anomalous dimensions of planar N = 4 supersymmetric Yang-Mills theory. Phys. Rev. Lett. 103, 131601 (2009). http://xxx. lanl. gov/abs/0901. 3753.
4. Zamolodchikov A. B.: Thermodynamic Bethe Ansatz in relativistic models. Scaling three state Potts and Lee-Yang models. Nucl. Phys. B 342, 695-720 (1990).
5. Bombardelli, D., Fioravanti, D., Tateo, R.: Thermodynamic Bethe Ansatz for planar AdS/CFT: a proposal. J. Phys. A 42, 375401 (2009). http://xxx. lanl. gov/abs/0902. 3930.
6. Gromov, N., Kazakov, V., Kozak, A., Vieira, P.: Exact spectrum of anomalous dimensions of planar N = 4 supersymmetric Yang-Mills theory: TBA and excited states. Lett. Math. Phys. 91, 265-287 (2010). http://xxx. lanl. gov/abs/0902. 4458.
7. 5 mirror model. JHEP 05, 068 (2009). http://xxx. lanl. gov/abs/0903. 0141.
8. Saleur, H.: The continuum limit of sl(N{pipe}K) integrable super spin chains. Nucl. Phys. B 578, 552-576 (2000). http://xxx. lanl. gov/abs/solv-int/9905007.
9. Essler, F. H. L., Frahm, H., Saleur, H.: Continuum limit of the integrable sl(2{pipe}1) 3-3̄ superspin chain. Nucl. Phys. B 712, 513-572 (2005). http://xxx. lanl. gov/abs/cond-mat/0501197.
10. Candu, C.: Continuum limit of gl(M/N) spin chains. JHEP 1107, 069 (2011). http://xxx. lanl. gov/abs/1012. 0050.
11. 4 correspondence. Nucl. Phys. B 843, 302-343 (2011). http://xxx. lanl. gov/abs/1005. 3016.
12. Gromov, N., Kazakov, V., Tsuboi, Z.: PSU(2, 2{pipe}4) character of quasiclassical AdS/CFT. JHEP 07, 097 (2010). http://xxx. lanl. gov/abs/1002. 3981.
13. Bethe H.: On the theory of metals. 1. Eigenvalues and eigenfunctions for the linear atomic chain. Z. Phys. 71, 205-226 (1931).
14. Faddeev L. D., Takhtajan L. A.: What is the spin of a spin wave?. Phys. Lett. A 85, 375-377 (1981).
15. Faddeev L. D., Takhtajan L. A.: Spectrum and scattering of excitations in the one-dimensional isotropic Heisenberg model. J. Sov. Math. 24, 241-267 (1984).
16. 5 mirror. JHEP 03, 152 (2009). http://xxx. lanl. gov/abs/0901. 1417.
17. Takahashi M.: One-dimensional Hubbard model at finite temperature. Prog. Theor. Phys. 47, 69 (1972).
18. Zinn-Justin, P.: Quelques applications de l'Ansatz de Bethe. http://xxx. lanl. gov/abs/solv-int/9810007 (in French).
19. Volin, D.: Quantum integrability and functional equations: applications to the spectral problem of AdS/CFT and two-dimensional sigma models. J. Phys. A 44, 124003 (2011). http://xxx. lanl. gov/abs/1003. 4725.
20. 5 mirror model. JHEP 11, 019 (2009). http://xxx. lanl. gov/abs/0907. 2647.
21. Bazhanov, V. V., Lukyanov, S. L., Zamolodchikov, A. B.: Quantum field theories in finite volume: excited state energies. Nucl. Phys. B 489, 487-531 (1997). http://xxx. lanl. gov/abs/hep-th/9607099.
22. Dorey, P., Tateo, R.: Excited states by analytic continuation of TBA equations. Nucl. Phys. B 482, 639-659 (1996). http://xxx. lanl. gov/abs/hep-th/9607167.
23. Destri C., de Vega H. J.: New thermodynamic Bethe ansatz equations without strings. Phys. Rev. Lett. 69, 2313-2317 (1992).
24. Destri, C., De Vega, H. J.: Unified approach to thermodynamic Bethe Ansatz and finite size corrections for lattice models and field theories. Nucl. Phys. B 438, 413-454 (1995). http://xxx. lanl. gov/abs/hep-th/9407117.
25. Fioravanti, D., Mariottini, A., Quattrini, E., Ravanini, F.: Excited state Destri-De Vega equation for Sine-Gordon and restricted Sine-Gordon models. Phys. Lett. B 390, 243-251 (1997). http://xxx. lanl. gov/abs/hep-th/9608091.
26. Frappat, L., Sorba, P., Sciarrino, A.: Dictionary on Lie superalgebras. http://xxx. lanl. gov/abs/hep-th/9607161.
27. Kulish P. P., Reshetikhin N. Y.: Diagonalization of Gl(N) invariant transfer matrices and quantum N wave system (Lee model). J. Phys. A16, L591-L596 (1983).
28. Ragoucy, E., Satta, G.: Analytical Bethe Ansatz for closed and open gl(M{pipe}N) super-spin chains in arbitrary representations and for any Dynkin diagram. JHEP 09, 001 (2007). http://xxx. lanl. gov/abs/0706. 3327.
29. Woynarovich F.: Low-energy excited states in a Hubbard chain with on-site attraction. J. Phys. C: Solid State Phys. 16, 6593 (1983).
30. Bares P.-A., Carmelo J. M. P., Ferrer J., Horsch P.: Charge-spin recombination in the one-dimensional supersymmetric t-J model. Phys. Rev. B 46, 14624-14654 (1992).
31. Tsuboi Z.: Analytic Bethe Ansatz and functional equations associated with any simple root systems of the Lie superalgebra SL(r+1{pipe}s+1). Physica A 252, 565-585 (1998).
32. Gohmann, F., Seel, A.: A note on the Bethe ansatz solution of the supersymmetric t-J model. http://xxx. lanl. gov/abs/cond-mat/0309138.
33. Pronko, G. P., Stroganov, Y. G.: Bethe equations "on the Wrong Side of Equator". J. Phys. A 32, 2333-2340 (1999). http://xxx. lanl. gov/abs/hep-th/9808153.
34. Gromov, N., Vieira, P.: Complete 1-loop test of AdS/CFT. JHEP 04, 046 (2008). http://xxx. lanl. gov/abs/0709. 3487.
35. Bazhanov, V. V., Tsuboi, Z.: Baxter's Q-operators for supersymmetric spin chains. Nucl. Phys. B 805, 451-516 (2008). http://xxx. lanl. gov/abs/0805. 4274.
36. Vladimirov A. A.: Proof of the invariance of the bethe-ansatz solutions under complex conjugation. Theor. Math. Phys. 66, 102-105 (1986). doi: 10. 1007/BF01028945.
37. Freyhult, L., Rej, A., Zieme, S.: From weak coupling to spinning strings. JHEP 02, 050 (2010). http://xxx. lanl. gov/abs/0911. 2458.
38. Zabrodin, A.: Backlund transformations for difference Hirota equation and supersymmetric Bethe ansatz. http://xxx. lanl. gov/abs/0705. 4006.
39. Cheng, S.-J., Lam, N., Zhang, R.: Character formula for infinite dimensional unitarizable modules of the general linear superalgebra. J. Algebra 273, 780 (2004). http://xxx. lanl. gov/abs/math/0301183.
40. Jakobsen, H. P.: The full set of unitarizable highest weight modules of basic classical lie superalgebras. Memoirs of A. M. S. no. 532 (1994).
41. Enright, T., Howe, R., Wallach, N.: A classification of unitary highest weight modules. Progress in Mathematics, vol. 40. Birkhäuser, Boston (1983).
42. Dobrev V. K., Petkova V. B.: All positive energy unitary irreducible representations of extended conformal supersymmetry. Phys. Lett. B 162, 127-132 (1985).
43. Derkachov, S. E., Manashov, A. N.: Factorization of R-matrix and Baxter Q-operators for generic sl(N) spin chains. J. Phys. A 42, 075204 (2009). http://xxx. lanl. gov/abs/0809. 2050.
44. Kazakov, V., Leurent, S., Tsuboi, Z.: Baxter's Q-operators and operatorial Backlund flow for quantum (super)-spin chains. Commun. Math. Phys. 311, 787-814 (2012). http://xxx. lanl. gov/abs/1010. 4022.
45. Bazhanov, V. V., Frassek, R., Lukowski, T., Meneghelli, C., Staudacher, M.: Baxter Q-operators and representations of Yangians. Nucl. Phys. B 850, 148-174 (2011). http://xxx. lanl. gov/abs/1010. 3699.
46. Gaiotto, D., Maldacena, J., Sever, A., Vieira, P.: Bootstrapping null polygon Wilson loops. JHEP 1103, 092 (2011). http://xxx. lanl. gov/abs/1010. 5009.
47. Basso, B.: Exciting the GKP string at any coupling. Nucl. Phys. B 857, 254-334 (2012). http://xxx. lanl. gov/abs/1010. 5237.
48. Kirrilov A.: Completeness of states of the generalised heisenberg magnet. J. Math. Sci. 36, 115-128 (1987).
49. Kirillov A.: Combinatorial identities, and completeness of eigenstates of the heisenberg magnet. J. Math. Sci. 30, 2298-2310 (1985). doi: 10. 1007/BF02105347.
50. Kerov S., Kirillov A., Reshetikhin N.: Combinatorics, the bethe ansatz and representations of the symmetric group. J. Sov. Math. 41, 916-924 (1988).
51. Isler, K., Paranjape, M. B.: Violations of the string hypothesis in the solutions of the Bethe ansatz equations in the XXX Heisenberg model. Phys. Lett. B 319, 209-214 (1993). http://xxx. lanl. gov/abs/hep-th/9304078.
52. Ilakovac, A., Kolanovic, M., Pallua, S., Prester, P.: Violation of the string hypothesis and Heisenberg XXZ spin chain. Phys. Rev. B 60, 7271 (1999). http://xxx. lanl. gov/abs/hep-th/9907103.
53. Bargheer, T., Beisert, N., Gromov, N.: Quantum stability for the Heisenberg ferromagnet. New J. Phys. 10, 103023 (2008). http://xxx. lanl. gov/abs/0804. 0324.
54. Antipov A., Komarov I.: The isotropic heisenberg chain of arbitrary spin by direct solution of the baxter equation. Physica D 221, 101-109 (2006).