Abstract
Using the Poisson current algebra of the supersymmetric principal chiral model, we develop the algebraic canonical structure of the model by evaluating the fundamental Poisson bracket of the Lax matrices that fits into the r–s matrix formalism of non-ultralocal integrable models. The fundamental Poisson bracket has been used to compute the Poisson bracket algebra of the monodromy matrix that gives the conserved quantities in involution.
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References
U. Saleem, M. Hassan, Eur. Phys. J. C 38, 521 (2005) [hep-th/0501124]
J.M. Evans, M. Hassan, N.J. MacKay, A.J. Mountain, Nucl. Phys. B 580, 605 (2000) [hep-th/0001222]
J.M. Evans, N.J. MacKay, M. Hassan, Nucl. Phys. B 561, 385 (1999) [hep-th/9711140]
T.L. Curtright, C.K. Zachos, Phys. Rev. D 21, 411 (1980)
L.L. Chau, H.C. Yen, Phys. Lett. B 177, 368 (1986)
T. Curtright, C.K. Zachos, Nucl. Phys. B 402, 604 (1993) [hep-th/9210060]
T. Curtright, C.K. Zachos, Phys. Rev. D 49, 5408 (1994) [hep-th/9401006]
U. Saleem, M. Hassan, Eur. Phys. J. C 46, 797 (2006) [hep-th/0605091]
J.M. Evans, C.A.S. Young, Nucl. Phys. B 717, 327 (2005) [hep-th/0501090]
R.D. Richtmyer, Principles of Advanced Mathematical Physics (Springer, Heidelberg, 1981), Vol. II
S.G. Rajeev, G. Sparano, P. Vitale, Int. J. Mod. Phys. A 9, 5469 (1994) [hep-th/9312178]
S.G. Rajeev, A. Stern, P. Vitale, Phys. Lett. B 388, 769 (1996) [hep-th/9602149]
M. Jimbo, Adv. Ser. Math. Phys. 10, 1 (1989)
M. Jimbo, T. Miwa, Physica D 4, 26 (1981)
L.D. Faddeev, L.A. Takhtajan, Hamiltonian Methods in the Theory of Solitons (Springer, Berlin, 1987), p. 592 (Springer Series in Soviet Mathematics)
J.H. Humphreys, Introduction to Lie Algebras and Representation Theory (Springer, Berlin, 1970), p. 169
J.M. Maillet, Nucl. Phys. B 269, 54 (1986)
H.J. de Vega, H. Eichenherr, J.M. Maillet, Nucl. Phys. B 240, 377 (1984)
H.J. de Vega, H. Eichenherr, J.M. Maillet, Commun. Math. Phys. 92, 507 (1984)
J.M. Maillet, Phys. Lett. B 162, 137 (1985)
J.M. Maillet, Phys. Lett. B 167, 401 (1986)
L.D. Faddeev, Integrable Models in (1+1)-dimensional Quantum Field Theory (Les Houches Summer School, 1982), p. 561
M. Forger, M. Bordemann, J. Laartz, U. Schaper, Commun. Math. Phys. 152, 167 (1993) [hep-th/9201051]
I. Bena, J. Polchinski, R. Roiban, Phys. Rev. D 69, 046002 (2004) [hep-th/0305116]
G. Arutyunov, J. Russo, A.A. Tseytlin, Phys. Rev. D 69, 086009 (2004) [hep-th/0311004]
M. Hatsuda, K. Yoshida, Adv. Theor. Math. Phys. 9, 703 (2005) [hep-th/0407044]
G. Mandal, N.V. Suryanarayana, S.R. Wadia, Phys. Lett. B 543, 81 (2002) [hep-th/0206103]
L.F. Alday, G. Arutyunov, A.A. Tseytlin, JHEP 0507, 002 (2005) [hep-th/0502240]
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11.30.Pb; 02.30.Ik
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Haider, B., Hassan, M. On algebraic structures in supersymmetric principal chiral model. Eur. Phys. J. C 53, 627–633 (2008). https://doi.org/10.1140/epjc/s10052-007-0483-4
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DOI: https://doi.org/10.1140/epjc/s10052-007-0483-4