From Integrability to Conformal Symmetry: Bosonic Superconformal Toda Theories

ZHAO Liu

Chinese Physics C> 1993, Vol. 17> Issue(5) : 431-443

From Integrability to Conformal Symmetry: Bosonic Superconformal Toda Theories

ZHAO Liu ^,

Institute of Modern Physics,Northwest University,Xi'an 710069

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Abstract：
In this paper we study the new conformal integrable models obtained from conformal reductions of WZNW theory associated with second order constraints,these models are called bosonic superconformal Toda models due to their conformal spectra and their resemblance to the usual Toda theories.From the reduction procedure we get the equations of motion and the linearized Lax equations for such systems in a generic gradation of the underlying Lie algebra.Then,in the special case of principal gradation,we derive the classical r-matrix,fundamental Poisson relation,exchange algebra of the chiral operators and find out the classical vertex operators.The result shows that our model may play a similar role with respect to the ordinary Toda theories in which one may obtainvarious conformal properties of the model from its integrability.

References

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O.Babelon, Phys. Lett.，215B(1988),523,Preprint PAR LPTHE89/29.[2]L.D. Faddeev and L. Takhtajan, Hamiltonian mathods in the theory of solitons, Springer Verlag(1987).[3]O. Babelon and C. M. Viallet, Integrable models, Yang-Baxter equations and quantum groups, Cambridge University Press(1991).[4]O. Babelon and D. Bernard ,Phys. Lett.，B260(1991),81.[5]A. Bilal and J-L. Gervais, Phys. Lett.，B206(1988),412; Nucl. Phys. B314(1989),646; Nucl. Phys.，B318(1989),579.[6]J. Balog, L. Feher, L. O' Raifeartaigh, P. Forgacs and A. Wipf, Ann. Phys.，203(1991),76.[7]L. O'Raifeartaigh and A. Wipf, DIAS-STP-90-19,ETH-TH/90-20: L.O'Raifeartaigh, DIAS-STP-90-43,DIAS-STP-90-45;L.O'Raifeartaigh, P. Ruelle, I. Tsutsui and A. Wipf, DIAS-STP-91-03;L. Feher. I.O'Raifeartaioh. P. Ruelle. I. Tsutsui and A. Wipf. DIAS-STP-91-17.[8]J. Fuchs, Phys. Lett. B262 (1991)249, F. A. Bias, T. Tjin, P. van Driel, Nucl. Phys.，B357(1991)，632[9]L. Chao, NWU/IMP/910525.[10]Hou Bo-yu and Chao Liu, NR'U/IMP/911115.[11]Hou Bo-yu and Chao Liu, NR'U/IMP/911117.

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ZHAO Liu. From Integrability to Conformal Symmetry: Bosonic Superconformal Toda Theories[J]. Chinese Physics C, 1993, 17(5): 431-443.

ZHAO Liu. From Integrability to Conformal Symmetry: Bosonic Superconformal Toda Theories[J]. Chinese Physics C, 1993, 17(5): 431-443. shu

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Received: 1900-01-01
Revised: 1900-01-01

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From Integrability to Conformal Symmetry: Bosonic Superconformal Toda Theories

ZHAO Liu ^,

Corresponding author: ZHAO Liu,

Institute of Modern Physics,Northwest University,Xi'an 710069

Received Date: 1900-01-01
Accepted Date: 1900-01-01
Available Online: 1993-05-05

Abstract: In this paper we study the new conformal integrable models obtained from conformal reductions of WZNW theory associated with second order constraints,these models are called bosonic superconformal Toda models due to their conformal spectra and their resemblance to the usual Toda theories.From the reduction procedure we get the equations of motion and the linearized Lax equations for such systems in a generic gradation of the underlying Lie algebra.Then,in the special case of principal gradation,we derive the classical r-matrix,fundamental Poisson relation,exchange algebra of the chiral operators and find out the classical vertex operators.The result shows that our model may play a similar role with respect to the ordinary Toda theories in which one may obtainvarious conformal properties of the model from its integrability.