Spin chains and string theory

Physical Review Letters

Volumn 93, Issue 16, 2004, Pages

  Kruczenski, Martin ^a  

^a BRANDEIS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANTIFERROMAGNETISM; BOUNDARY CONDITIONS; CONFORMAL MAPPING; CONTINUUM MECHANICS; EQUATIONS OF MOTION; FUNCTIONS; HAMILTONIANS; HIGH ENERGY PHYSICS; INTEGRAL EQUATIONS; MATHEMATICAL OPERATORS; SET THEORY;

CONFORMAL FIELD THEORY (CFT); CYCLIC PERMUTATIONS; SPIN CHAINS; STRING THEORY;

FERROMAGNETISM;

EID: 19644401420     PISSN: 00319007     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevLett.93.161602     Document Type: Article

References (41)

1. J. Maldacena, Adv. Theor. Math. Phys. 2, 231 (1998); Int. J. Theor. Phys. 38, 1113 (1999); S.S. Gubser, I. R. Klebanov, and A. M. Polyakov, Phys. Lett. B 428, 105 (1998); E. Witten, Adv. Theor. Math. Phys. 2, 253 (1998); O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri, and Y Oz, Phys. Rep. C323, 183 (2000).
2. J. Maldacena, Adv. Theor. Math. Phys. 2, 231 (1998); Int. J. Theor. Phys. 38, 1113 (1999); S.S. Gubser, I. R. Klebanov, and A. M. Polyakov, Phys. Lett. B 428, 105 (1998); E. Witten, Adv. Theor. Math. Phys. 2, 253 (1998); O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri, and Y Oz, Phys. Rep. C323, 183 (2000).
3. J. Maldacena, Adv. Theor. Math. Phys. 2, 231 (1998); Int. J. Theor. Phys. 38, 1113 (1999); S.S. Gubser, I. R. Klebanov, and A. M. Polyakov, Phys. Lett. B 428, 105 (1998); E. Witten, Adv. Theor. Math. Phys. 2, 253 (1998); O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri, and Y Oz, Phys. Rep. C323, 183 (2000).
4. J. Maldacena, Adv. Theor. Math. Phys. 2, 231 (1998); Int. J. Theor. Phys. 38, 1113 (1999); S.S. Gubser, I. R. Klebanov, and A. M. Polyakov, Phys. Lett. B 428, 105 (1998); E. Witten, Adv. Theor. Math. Phys. 2, 253 (1998); O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri, and Y Oz, Phys. Rep. C323, 183 (2000).
5. J. Maldacena, Adv. Theor. Math. Phys. 2, 231 (1998); Int. J. Theor. Phys. 38, 1113 (1999); S.S. Gubser, I. R. Klebanov, and A. M. Polyakov, Phys. Lett. B 428, 105 (1998); E. Witten, Adv. Theor. Math. Phys. 2, 253 (1998); O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri, and Y Oz, Phys. Rep. C323, 183 (2000).
6. G.'t Hooft, Nucl. Phys. B72, 461 (1974); G.'t Hooft, Nucl. Phys. B75, 461 (1974).
7. G.'t Hooft, Nucl. Phys. B72, 461 (1974); G.'t Hooft, Nucl. Phys. B75, 461 (1974).
8. D. Berenstein, J. M. Maldacena, and H. Nastase, J. High Energy Phys. 04 (2002) 013.
9. S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, Nucl. Phys. B636, 99 (2002).
10. See A.A. Tseytlin, hep-th/0311139 for a review and references to the original literature.
11. J. A. Minahan and K. Zarembo, J. High Energy Phys. 03 (2003) 013.
12. V. M. Braun, S. E. Derkachov, and A. N. Manashov, Phys. Rev. Lett. 81, 2020 (1998); V. M. Braun, S. E. Derkachov, G. P. Korchemsky, and A. N. Manashov, Nucl. Phys. B553, 355 (1999); A.V. Belitsky, Nucl. Phys. B558, 259 (1999); Phys. Lett. B 453, 59 (1999).
13. V. M. Braun, S. E. Derkachov, and A. N. Manashov, Phys. Rev. Lett. 81, 2020 (1998); V. M. Braun, S. E. Derkachov, G. P. Korchemsky, and A. N. Manashov, Nucl. Phys. B553, 355 (1999); A.V. Belitsky, Nucl. Phys. B558, 259 (1999); Phys. Lett. B 453, 59 (1999).
14. V. M. Braun, S. E. Derkachov, and A. N. Manashov, Phys. Rev. Lett. 81, 2020 (1998); V. M. Braun, S. E. Derkachov, G. P. Korchemsky, and A. N. Manashov, Nucl. Phys. B553, 355 (1999); A.V. Belitsky, Nucl. Phys. B558, 259 (1999); Phys. Lett. B 453, 59 (1999).
15. V. M. Braun, S. E. Derkachov, and A. N. Manashov, Phys. Rev. Lett. 81, 2020 (1998); V. M. Braun, S. E. Derkachov, G. P. Korchemsky, and A. N. Manashov, Nucl. Phys. B553, 355 (1999); A.V. Belitsky, Nucl. Phys. B558, 259 (1999); Phys. Lett. B 453, 59 (1999).
16. N. Beisert, J. A. Minahan, M. Staudacher, and K. Zarembo, J. High Energy Phys. 09 (2003) 010.
17. N. Beisert, C. Kristjansen, and M. Staudacher, Nucl. Phys. B664 (2003)131.
18. N. Beisert, S. Frolov, M. Staudacher, and A. A. Tseytlin, J. High Energy Phys. 10 (2003) 037.
19. S. Frolov and A. A. Tseytlin, Phys. Lett. B 570, 96 (2003).
20. G. Arutyunov and M. Staudacher, J. High Energy Phys. 03 (2004) 004.
21. G. Arutyunov, J. Russo, and A. A. Tseytlin, Phys. Rev. D 69, 086009 (2004).
22. G. Arutyunov, S. Frolov, J. Russo, and A. A. Tseytlin, Nucl. Phys. B671, 3 (2003).
23. T. Holstein and H. Primakoff, Phys. Rev. 58, 1098, (1940); P.W. Anderson, Phys. Rev. 86, 694, (1952); N. Read and S. Sachdev, Phys. Rev. Lett. 75, 3509, (1995); A. Dhar and B.S. Shastry, Phys. Rev. Lett.85, 2813 (2000).
24. T. Holstein and H. Primakoff, Phys. Rev. 58, 1098, (1940); P.W. Anderson, Phys. Rev. 86, 694, (1952); N. Read and S. Sachdev, Phys. Rev. Lett. 75, 3509, (1995); A. Dhar and B.S. Shastry, Phys. Rev. Lett.85, 2813 (2000).
25. T. Holstein and H. Primakoff, Phys. Rev. 58, 1098, (1940); P.W. Anderson, Phys. Rev. 86, 694, (1952); N. Read and S. Sachdev, Phys. Rev. Lett. 75, 3509, (1995); A. Dhar and B.S. Shastry, Phys. Rev. Lett.85, 2813 (2000).
26. T. Holstein and H. Primakoff, Phys. Rev. 58, 1098, (1940); P.W. Anderson, Phys. Rev. 86, 694, (1952); N. Read and S. Sachdev, Phys. Rev. Lett. 75, 3509, (1995); A. Dhar and B.S. Shastry, Phys. Rev. Lett.85, 2813 (2000).
27. E. Fradkin, Field Theories of Condensed Matter Systems (Addison-Wesley, Reading, MA, 1991).
28. See also M. Kruczenski, A. V. Ryzhov, and A. A. Tseytlin, hep-th/0403120.
29. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals Series and Products (Academic, New York, 2000), 6th ed.
30. V. M. Braun, S. E. Derkachov, and A. N. Manashov, Phys. Rev. Lett.81, 2020 (1998); V. M. Braun, S. E. Derkachov, G.P. Korchemsky, and A.N. Manashov, Nucl. Phys. B553, 355 (1999); A.V. Belitsky, Nucl. Phys. B558, 259 (1999); Phys. Lett. B 453, 59 (1999).
31. V. M. Braun, S. E. Derkachov, and A. N. Manashov, Phys. Rev. Lett.81, 2020 (1998); V. M. Braun, S. E. Derkachov, G.P. Korchemsky, and A.N. Manashov, Nucl. Phys. B553, 355 (1999); A.V. Belitsky, Nucl. Phys. B558, 259 (1999); Phys. Lett. B 453, 59 (1999).
32. V. M. Braun, S. E. Derkachov, and A. N. Manashov, Phys. Rev. Lett.81, 2020 (1998); V. M. Braun, S. E. Derkachov, G.P. Korchemsky, and A.N. Manashov, Nucl. Phys. B553, 355 (1999); A.V. Belitsky, Nucl. Phys. B558, 259 (1999); Phys. Lett. B 453, 59 (1999).
33. V. M. Braun, S. E. Derkachov, and A. N. Manashov, Phys. Rev. Lett.81, 2020 (1998); V. M. Braun, S. E. Derkachov, G.P. Korchemsky, and A.N. Manashov, Nucl. Phys. B553, 355 (1999); A.V. Belitsky, Nucl. Phys. B558, 259 (1999); Phys. Lett. B 453, 59 (1999).
34. U. H. Danielsson, A. Guijosa, and M. Kruczenski, J. High Energy Phys. 10 (2000) 020; J. Gomis and H. Ooguri, J. Math. Phys. (N.Y.) 42, 3127 (2001).
35. U. H. Danielsson, A. Guijosa, and M. Kruczenski, J. High Energy Phys. 10 (2000) 020; J. Gomis and H. Ooguri, J. Math. Phys. (N.Y.) 42, 3127 (2001).
36. A. Gorsky, hep-th/0308182.
37. A. Mikhailov, J. High Energy Phys. 12 (2003) 058.
38. D. Mateos, T. Mateos, and P. K. Townsend, J. High Energy Phys. 12 (2003) 017.
39. N. Beisert, Nucl. Phys. B676, 3 (2004).
40. In QCD the relation between spin chains and anomalous dimensions had already been noted in [7].
41. It also has some similarities with the so called wrapped or nonrelativistic limit [20]. For the present case some related ideas appeared in [21,22]