Review of AdS/CFT Integrability, Chapter III.1: Bethe Ansätze and the R-Matrix Formalism

Letters in Mathematical Physics

Volumn 99, Issue 1-3, 2012, Pages 191-208

  Staudacher, Matthias ^a,b  

^a HUMBOLDT UNIVERSITY   (Germany)

^b ALBERT EINSTEIN INSTITUT   (Germany)

Author keywords

Bethe ansatz; Q operator; R matrix

Indexed keywords

EID: 84856208960     PISSN: 03779017     EISSN: 15730530     Source Type: Journal    
DOI: 10.1007/s11005-011-0530-9     Document Type: Review

References (28)

1. Bethe H.: Zur theorie der metalle I Eigenwerte und Eigenfunktionen der linearen atomkette. Z. Phys. 71, 205-226 (1931).
2. Beisert, N.: Review of AdS/CFT Integrability, Chapter VI. 1: Superconformal Algebra. Lett. Math. Phys. Published in this volume. arXiv: 1012. 4004 [hep-th].
3. Nepomechie R. I.: A spin chain primer. Int. J. Mod. Phys. B 13, 2973-2986 (1999). doi: 10. 1142/S0217979299002800 arXiv: hep-th/9810032.
4. Schafer-Nameki, S.: Review of AdS/CFT Integrability, Chapter II. 4: The Spectral Curve. Lett. Math. Phys. Published in this volume. arXiv: 1012. 3989 [hep-th].
5. Korepin V., Bogoliubov N., Izergin A.: Quantum Inverse Scattering Method and Correlation Functions. Cambridge University Press, Cambridge (1993).
6. Karbach M., Müller G.: Introduction to the Bethe ansatz I. Computers in Physics 11, 36 (1997) arXiv: cond-mat/9809162.
7. Staudacher M.: The factorized S-matrix of CFT/AdS. JHEP 05, 054 (2005) arXiv: hep-th/0412188.
8. Sutherland B.: A brief history of the quantum soliton with new results on the quantization of the Toda lattice. Rocky Mt. J. Math. 8, 431 (1978).
9. Sutherland B.: Beautiful Models: 70 Years of Exactly Solved Quantum Many-Body Problems. World Scientific, New Jersey (2004).
10. Faddeev, L. D.: How Algebraic Bethe Ansatz works for integrable model. arXiv: hep-th/9605187.
11. Faddeev L. D.: Algebraic aspects of Bethe Ansatz. Int. J. Mod. Phys. A 10, 1845-1878 (1995). doi: 10. 1142/S0217751X95000905 arXiv: hep-th/9404013.
12. Doikou, A., Evangelisti, S., Feverati, G., Karaiskos, N.: Introduction to Quantum Integrability. arXiv: 0912. 3350 [math-ph].
13. Escobedo, J., Gromov, N., Sever, A., Vieira, P.: Tailoring Three-Point Functions and Integrability. arXiv: 1012. 2475 [hep-th].
14. Zoubos, K.: Review of AdS/CFT Integrability, Chapter IV. 2: Deformations, Orbifolds and Open Boundaries. Lett. Math. Phys. Published in this volume. arXiv: 1012. 3998 [hep-th].
15. Minahan, J. A.: Review of AdS/CFT Integrability, Chapter I. 1: Spin Chains in N = 4 SYM. Lett. Math. Phys. Published in this volume. arXiv: 1012. 3983 [hep-th].
16. Sutherland, B.: Exactly Solvable Problems in Condensed Matter and Relativistic Field Theory. Lecture Notes in Physics, vol. 242. Springer, Berlin (1985).
17. Sutherland B.: A general model for multicomponent quantum systems. Phys. Rev. B 12, 3795-3805 (1975). doi: 10. 1103/PhysRevB. 12. 3795.
18. Rej, A.: Review of AdS/CFT Integrability, Chapter I. 3: Long-range spin chains. Lett. Math. Phys. Published in this volume. arXiv: 1012. 3985 [hep-th].
19. Sieg, C.: Review of AdS/CFT Integrability, Chapter I. 2: The spectrum from perturbative gauge theory. Lett. Math. Phys. Published in this volume. arXiv: 1012. 3984 [hep-th].
20. Janik, R.: Review of AdS/CFT Integrability, Chapter III. 5: Lüscher corrections. Lett. Math. Phys. Published in this volume. arXiv: 1012. 3994 [hep-th].
21. Ahn, C., Nepomechie, R. I.: Review of AdS/CFT Integrability, Chapter III. 2: Exact world-sheet S-matrix. Lett. Math. Phys. Published in this volume. arXiv: 1012. 3991 [hep-th].
22. Vieira, P., Volin, D.: Review of AdS/CFT Integrability, Chapter III. 3: The dressing factor. Lett. Math. Phys. Published in this volume. arXiv: 1012. 3992 [hep-th].
23. 5 superstring. arXiv: 1007. 4931 [hep-th].
24. Kazakov, V., Gromov, N.: Review of AdS/CFT Integrability, Chapter III. 7: Hirota Dynamics for Quantum Integrability. Lett. Math. Phys. Published in this volume. arXiv: 1012. 3996 [hep-th].
25. Bajnok, Z.: Review of AdS/CFT Integrability, Chapter III. 6: Thermodynamic Bethe Ansatz. Lett. Math. Phys. Published in this volume. arXiv: 1012. 3995 [hep-th].
26. Bazhanov V. V., Łukowski T., Meneghelli C., Staudacher M.: A Shortcut to the Q-Operator. J. Stat. Mech. 1011, P11002 (2010). doi: 10. 1088/1742-5468/2010/11/P11002 arXiv: 1005. 3261 [hep-th].
27. Bazhanov, V. V., Frassek, R., Lukowski, T., Meneghelli, C., Staudacher, M.: Baxter Q-Operators and Representations of Yangians. arXiv: 1010. 3699 [math-ph].
28. Frassek, R., Łukowski, T., Meneghelli, C., Staudacher, M.: Oscillator Construction of su(n{pipe}m) Q-Operators. arXiv: 1012. 6021 [math-ph].