From Integrability to Conformal Symmetry: Bosonic Superconformal Toda Theories

ZHAO Liu

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2024年10月30日

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

[1]

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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[2]	Sayipjamal Dulat . Z₂ Orbifold-Prime Model of N=2 Superconformal Theories with c=3. Chinese Physics C, 2003, 27(5): 386-390.
[3]	YANG ZhanYing , ZHEN Yi . Construction on the Solution of osp(1｜4)Toda Model. Chinese Physics C, 2000, 24(6): 484-489.
[4]	Xi Xiaoqiang , Shi Kangjie , Hou Boyu , Fan Heng . Algebraic Bethe Ansatz for the Supersymmetric t-J Model With Reflecting Boundary Conditions in FBF Background. Chinese Physics C, 1999, 23(10): 961-979.
[5]	Wang Deyun , Huang Bowen . Solve for Energy Spectrum and Function of Ring-Shaped Oscillator by Using Supersymmetry and Shape Invariance. Chinese Physics C, 1999, 23(11): 1078-1082.
[6]	Yang Kongqing , Luo Yan . Conformal Transformation and Symplectic Structure of Self-Dual Fields. Chinese Physics C, 1996, 20(9): 789-793.
[7]	Yue Ruihong , Liang Hong . Integrability and Boundary Conditions of Supersymmetric Systems. Chinese Physics C, 1996, 20(6): 514-521.
[8]	Hu Zhanning , Hou Boyu . The Integrability Condition of Three-Dimensional Exactly Solvable Model-Baxter-Bazhanov Model in Statistical Mechanics. Chinese Physics C, 1995, 19(2): 123-130.
[9]	CHEN Yong-Qing . q-Oscillator Representations of the Quantum Superalgebra spl_q(2,1). Chinese Physics C, 1993, 17(7): 631-635.
[10]	Zhao Liu , Yang Wenli . Bosonic Superconformal Toda Theory and Dressing Symmetry. Chinese Physics C, 1993, 17(S1): 65-72.
[11]	HOU Bo-Yu , ZHAO Liu . Conformally Reduced WZNW Theory,New Extended Chiral Algebras and Their Associated Toda Type Integrable Systems (Ⅰ) General Framework. Chinese Physics C, 1993, 17(1): 28-37.
[12]	HOU Bo-Yu , ZHAO Liu . Conformally Reduced WZNW Theory,New Extended Chiral Algebras and Their Associated Toda Type Integrable Systems (Ⅱ)An Example. Chinese Physics C, 1993, 17(3): 241-251.
[13]	ZHAO Liu , YANG Wen-Li . Bosonic Superconformal Toda Model and Dressing Transformation. Chinese Physics C, 1993, 17(4): 338-344.
[14]	HOU Bo-Yu , ZHAO Liu , YANG Huan-Xiong . Affine Toda Fields as Restriced WZNW Model. Chinese Physics C, 1991, 15(8): 701-710.
[15]	YU Qing-Chang . A DISCUSSION OF TRANSFORMATIONS OF STRIP ION BEAMS INTO AXISYMMETRICAL BEAMS. Chinese Physics C, 1989, 13(2): 106-108.
[16]	HAO San-Ru , LI Wei . INFINITE CONFORMAL SYMMETRIES AND RIEMANN-HILBERT TRANSFORMATION IN SUPER PRINCIPAL CHIRAL MODEL. Chinese Physics C, 1989, 13(4): 320-327.
[17]	CHEN Wei . ALTERNATIVE REGULARIZATION SCHEME AND CONFORMAL ANOMALY IN STRINGS. Chinese Physics C, 1988, 12(5): 715-720.
[18]	XU Bo-Wei . VACUUM SOLUTIONS OF CONFORMALLY COVARIANT EQUATION FOR SYMMETRIC TENSOR FIELD. Chinese Physics C, 1985, 9(2): 241-243.
[19]	YU Qing-Chang . THE MUTUAL TRANSFORMATION OF STRIP ION BEAMS AND AXISYMMETRICAL ION BEAMS. Chinese Physics C, 1984, 8(2): 191-198.
[20]	XU Bo-Wei , . VACUUM SOLUTIONS OF CONFORMALLY COVARIANT NONLINEAR COUPLED EQUATIONS. Chinese Physics C, 1984, 8(1): 34-38.

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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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沈阳化工大学材料科学与工程学院沈阳 110142

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.