从可积条件到共形对称:玻色超共形Toda模型

From Integrability to Conformal Symmetry: Bosonic Superconformal Toda Theories

本文研究从WZNW模型的二阶共形约化得到的新模型一玻色超共形Toda模型.从约化过程得出了模型的运动方程及Lax pair线性方程组,进而在主阶化的特殊情形下求出了r矩阵、基本Poisson关系.手征交换代数以及经典顶角算子.

In this paper we study the new corformal 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 obtain various conformal properties of the model from its integrability.