A nonlocal Poisson bracket of the sine-Gordon model

Journal of Geometry and Physics

Volumn 61, Issue 1, 2011, Pages 85-94

  Mikhailov, Andrei ^a,b  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b INSTITUTE FOR THEORETICAL AND EXPERIMENTAL PHYSICS   (Russian Federation)

Author keywords

AdS CFT correspondence; Classical string theory; Poisson brackets; Sine Gordon model

Indexed keywords

EID: 77957269972     PISSN: 03930440     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.geomphys.2010.05.011     Document Type: Article

References (30)

1. Pohlmeyer K. Integrable Hamiltonian systems and interactions through quadratic constraints. Comm. Math. Phys. 1976, 46:207-221.
2. Gorsky A., Marshakov A., Orlov A., Rubtsov V. On third Poisson structure of KdV equation. Theoret. Math. Phys. 1995, 103:701-705. hep-th/9503018.
3. Maltsev A.Y., Novikov S.P. On the local systems Hamiltonian in the weakly non-local Poisson brackets. Physica D 2001, 156(1-2):53-80.
4. Zarembo K. Semiclassical Bethe ansatz and AdS/CFT. C.R. Phys. 2004, 5:1081-1090. hep-th/0411191.
5. Fridling B.E., Jevicki A. Dual representations and ultraviolet divergences in nonlinear sigma models. Phys. Lett. B 1984, 134:70.
6. Fradkin E.S., Tseytlin A.A. Quantum equivalence of dual field theories. Ann. Phys. 1985, 162:31.
7. de la Ossa X., Quevedo F. Duality symmetries from nonabelian isometries in string theory. Nuclear Phys. B 1993, 403:377-394. hep-th/9210021.
8. Curtright T., Zachos C.K. Canonical nonabelian dual transformations in supersymmetric field theories. Phys. Rev. D 1995, 52:573-576. hep-th/9502126.
9. Doliwa A., Santini P.M. An Elementary geometric characterization of the integrable motions of a curve. Phys. Lett. A 1994, 185:373-384.
10. Langer J. Recursion in curve geometry. New York J. Math. 1999, 5:25-51. (electronic).
11. Langer J., Perline R. Poisson geometry of the filament equation. J. Nonlinear Sci. 1991, 1(1):71-93.
12. Marí Beffa G., Sanders J.A., Wang J.P. Integrable systems in three-dimensional Riemannian geometry. J. Nonlinear Sci. 2002, 12(2):143-167.
13. Sanders J.A., Wang J.P. Integrable systems in n-dimensional Riemannian geometry. Mosc. Math. J. 2003, 3(4):1369-1393.
14. Marí Beffa G. Poisson brackets associated to invariant evolutions of Riemannian curves. Pacific J. Math. 2004, 215(2):357-380.
15. Marí Beffa G. Poisson brackets associated to the conformal geometry of curves. Trans. Amer. Math. Soc. 2005, 357(7):2799-2827. (electronic).
16. Marí Beffa G. Poisson geometry of differential invariants of curves in some nonsemisimple homogeneous spaces. Proc. Amer. Math. Soc. 2006, 134(3):779-791. (electronic).
17. Anco S.C. Bi-Hamiltonian operators, integrable flows of curves using moving frames and geometric map equations. J. Phys. A 2006, 39(9):2043-2072.
18. Anco S.C. Group-invariant soliton equations and bi-Hamiltonian geometric curve flows in Riemannian symmetric spaces. J. Geom. Phys. 2008, 58(1):1-37.
19. A. Mikhailov, BiHamiltonian structure of the classical superstring in AdS5×S5. arxiv:hep-th/0609108.
20. Bena I., Polchinski J., Roiban R. Hidden symmetries of the AdS(5)×S**5 superstring. Phys. Rev. D 2004, 69:046002. hep-th/0305116.
21. N. Beisert, V.A. Kazakov, K. Sakai, K. Zarembo, The algebraic curve of classical superstrings on AdS(5)×S**5. arxiv:hep-th/0502226.
22. Neveu A., Papanicolaou N. Integrability of the classical scalar and symmetric scalar-pseudoscalar contact Fermi interactions in two-dimensions. Comm. Math. Phys. 1978, 58:31.
23. Papanicolaou N. Gravitational duality and Bäcklund transformations. J. Math. Phys. 1979, 20:2069.
24. Fokas A.S., Olver P.J., Rosenau P. A plethora of integrable bi-Hamiltonian equations. Progr. Nonlinear Differential Equations Appl. 1997, 26:93-101.
25. Olver P. Applications of Lie Groups to Differential Equations 1986, Springer, New York.
26. Faddeev L.D., Takhtajan L.A. Hamiltonian Methods in the Theory of Solitons 1987, Springer.
27. Berenstein D., Maldacena J., Nastase H. Strings in flat space and PP-waves from N=4 super Yang-Mills. J. High Energy Phys. 2002, 0204:013. arxiv:hep-th/0202021.
28. Klimčík C., Ševera P. Dual nonabelian duality and the Drinfeld double. Phys. Lett. B 1995, 351:455-462. hep-th/9502122.
29. Lozano Y. Nonabelian duality and canonical transformations. Phys. Lett. B 1995, 355:165-170. hep-th/9503045.
30. Sfetsos K. Canonical equivalence of nonisometric sigma models and Poisson-Lie T duality. Nuclear Phys. B 1998, 517:549-566. hep-th/9710163.