Review of AdS/CFT Integrability, Chapter III.2: Exact World-Sheet S-Matrix

Letters in Mathematical Physics

Volumn 99, Issue 1-3, 2012, Pages 209-229

  Ahn, Changrim ^a   Nepomechie, Rafael I ^b  

^a Ewha Womans University   (South Korea)

^b UNIVERSITY OF MIAMI   (United States)

Author keywords

AdS CFT; Bethe ansatz; exact S matrix; Yang Baxter equation

Indexed keywords

EID: 84856152238     PISSN: 03779017     EISSN: 15730530     Source Type: Journal    
DOI: 10.1007/s11005-011-0478-9     Document Type: Review

References (49)

1. Zamolodchikov A. B., Zamolodchikov Al. B.: Factorized S matrices in two-dimensions as the exact solutions of certain relativistic quantum field models. Ann. Phys. 120, 253 (1979).
2. Staudacher M.: The factorized S-matrix of CFT/AdS. JHEP 0505, 054 (2005) arXiv: hep-th/0412188.
3. Beisert N.: The su(2{pipe}2) dynamic S-matrix. Adv. Theor. Math. Phys. 12, 945 (2008) arXiv: hep-th/0511082.
4. Beisert N.: The analytic Bethe ansatz for a chain with centrally extended su(2{pipe}2) symmetry. J. Stat. Mech. 0701, P017 (2007) arXiv: nlin/0610017.
5. 5 superstring worldsheet S-matrix and crossing symmetry. Phys. Rev. 7D3, 086006 (2006) arXiv: hep-th/0603038.
6. 5 string S-matrix. Phys. Lett. B639, 378 (2006) arXiv: hep-th/0604043.
7. 5 strings. JHEP 0611, 070 (2006) arXiv: hep-th/0609044.
8. Beisert N., Eden B., Staudacher M.: Transcendentality and crossing. J. Stat. Mech. 0701, P021 (2007) arXiv: hep-th/0610251.
9. 5 superstring. JHEP 0704, 002 (2007) arXiv: hep-th/0612229.
10. Beisert N., Staudacher M.: Long-range PSU(2, 2{pipe}4) Bethe ansaetze for gauge theory and strings. Nucl. Phys. B 727, 1 (2005) arXiv: hep-th/0504190.
11. Martins M. J., Melo C. S.: The Bethe ansatz approach for factorizable centrally extended S-matrices. Nucl. Phys. B 785, 246 (2007) arXiv: hep-th/0703086.
12. de Leeuw M.: Coordinate Bethe ansatz for the string S-matrix. J. Phys. A 40, 14413 (2007) arXiv: 0705. 2369.
13. 5. Lett. Math. Phys. (to appear). arXiv: 1012. 3987 [hep-th].
14. Magro, M.: Review of AdS/CFT Integrability, Chapter II. 3: Sigma Model, Gauge Fixing. Lett. Math. Phys. (to appear). arXiv: 1012. 3988 [hep-th].
15. Minahan J. A., Zarembo K.: The Bethe-Ansatz for N = 4 super Yang-Mills. JHEP 0303, 013 (2003) arXiv: hep-th/0212208.
16. Berenstein D., Vázquez S. E.: Integrable open spin chains from giant gravitons. JHEP 0506, 059 (2005) arXiv: hep-th/0501078.
17. Rej, A.: Review of AdS/CFT Integrability, Chapter I. 3: Long-Range Spin Chains. Lett. Math. Phys. (to appear). arXiv: 1012. 3985 [hep-th].
18. 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).
19. Faddeev L. D.: Quantum completely integral models of field theory. Sov. Sci. Rev. C1, 107 (1980).
20. Arutyunov G., Frolov S.: The S-matrix of string bound states. Nucl. Phys. B 804, 90 (2008) arXiv: 0803. 4323 [hep-th].
21. Kulish P. P., Reshetikhin N. Yu.: Quantum linear problem for the sine-Gordon equation and higher representation. J. Sov. Math. 23, 2435 (1983).
22. Zamolodchikov A. B.: Fractional-spin integrals of motion in perturbed conformal field theory. In: Guo, H., Qiu, Z., Tye, H. (eds) Fields, Strings and Quantum Gravity, Gordon and Breach, New York (1989).
23. Bernard D., Leclair A.: Quantum group symmetries and nonlocal currents in 2-D QFT. Commun. Math. Phys. 142, 99 (1991).
24. Santambrogio A., Zanon D.: Exact anomalous dimensions of N = 4 Yang-Mills operators with large R charge. Phys. Lett. B 545, 425 (2002) arXiv: hep-th/0206079.
25. Vieira, P., Volin, D.: Review of AdS/CFT Integrability, Chapter III. 3: The Dressing Factor. Lett. Math. Phys. (to appear). arXiv: 1012. 3992 [hep-th].
26. Shastry B. S.: Exact integrability of the one-dimensional Hubbard model. Phys. Rev. Lett. 56, 2453 (1986).
27. Shastry B. S.: Decorated star-triangle relations and exact integrability of the one-dimensional Hubbard model. J. Stat. Phys. 50, 57 (1988).
28. Dorey N.: Magnon bound states and the AdS/CFT correspondence. J. Phys. A39, 13119 (2006) arXiv: hep-th/0604175.
29. Chen H. Y., Dorey N., Okamura K.: On the scattering of magnon boundstates. JHEP 0611, 035 (2006) arXiv: hep-th/0608047.
30. Beisert, N.: The S-matrix of AdS/CFT and Yangian symmetry. PoS(SOLVAY) 002 (2006). arXiv: 0704. 0400.
31. Torrielli, A.: Review of AdS/CFT Integrability, Chapter VI. 2: Yangian Algebra. Lett. Math. Phys. (to appear). arXiv: 1012. 4005 [hep-th].
32. 5 superstring. JHEP 0806, 085 (2008) arXiv: 0804. 1047 [hep-th].
33. 5 superstring. Nucl. Phys. B 819, 319 (2009) arXiv: 0902. 0183 [hep-th].
34. Janik, R. A.: Review of AdS/CFT Integrability, Chapter III. 5: Lüscher Corrections. Lett. Math. Phys. (to appear). arXiv: 1012. 3994 [hep-th].
35. Yang C. N.: Some exact results for the many body problems in one dimension with repulsive delta function interaction. Phys. Rev. Lett. 19, 1312 (1967).
36. Gaudin M.: Un système à une dimension de fermions en interaction. Phys. Lett. A24, 55 (1967).
37. Gaudin M.: La fonction d'onde de Bethe. Masson, Paris (1983).
38. Andrei N., Furuya K., Lowenstein J. H.: Solution of the Kondo problem. Rev. Mod. Phys. 55, 331 (1983).
39. Arutyunov G., Frolov S.: On string S-matrix, bound states and TBA. JHEP 0712, 024 (2007) arXiv: 0710. 1568 [hep-th].
40. Faddeev, L. D.: How algebraic Bethe ansatz works for integrable model. arXiv: hep-th/9605187.
41. Nepomechie R. I.: A spin chain primer. Int. J. Mod. Phys. B 13, 2973 (1999) arXiv: hep-th/9810032.
42. Staudacher, M.: Review of AdS/CFT Integrability, Chapter III. 1: Bethe Ansätze and the R-Matrix Formalism. Lett. Math. Phys. (to appear). arXiv: 1012. 3990 [hep-th].
43. Beisert N., Roiban R.: Beauty and the twist: the Bethe ansatz for twisted N = 4 SYM. JHEP 0508, 039 (2005) arXiv: hep-th/0505187.
44. Ahn C., Nepomechie R. I.: N = 4 6 super Chern-Simons theory S-matrix and all-loop Bethe ansatz equations. JHEP 0809, 010 (2008) arXiv: 0807. 1924 [hep-th].
45. Gromov N., Vieira P.: The all loop AdS4/CFT3 Bethe ansatz. JHEP 0901, 016 (2009) arXiv: 0807. 0777 [hep-th].
46. Bajnok, Z.: Review of AdS/CFT Integrability, Chapter III. 6: Thermodynamic Bethe Ansatz. Lett. Math. Phys. (to appear). arXiv: 1012. 3995 [hep-th].
47. Ahn C., Bajnok Z., Bombardelli D., Nepomechie R. I.: Twisted Bethe equations from a twisted S-matrix. JHEP 1102, 027 (2011) arXiv: 1010. 3229 [hep-th].
48. Zoubos, K.: Review of AdS/CFT Integrability, Chapter IV. 2: Deformations, Orbifolds and Open Boundaries. Lett. Math. Phys. (to appear). arXiv: 1012. 3998 [hep-th].
49. 3. Lett. Math. Phys. (to appear). arXiv: 1012. 3999 [hep-th].