论文标题
综合理论的网
Webs of integrable theories
论文作者
论文摘要
我们提出了新的一类可集成的$ \ s $模型的直观图表表示。结果表明，在任何给定图中，都对应着一个可集成的理论，即$ n $ wzw型号与以下四个基本可集成的型号中的每一个中的一定数量，即PCM，PCM，YB型号，均基于$ g $，同型$ \ s $ \ s $ -mmodel在Symmetric Space $ g/h $ g/h $ g/h $ g/h $ g/h $ g/h $ h $ h $ h $上。对于图的每个顶点，我们分配了上述基本可整合理论之一的矩阵。任何两个顶点都可以与许多具有方向并携带整数级别$ k_i $的线连接。这些行中的每一行都与任意级别$ k_i $的不对称测量WZW模型相关联。完整动作的规格不变性将转化为顶点的水平保护。我们还展示了如何立即从图表中读取相应的$ \ s $模型操作。这些模型中最通用的取决于至少$ n^2+1 $参数，其中$ n $是顶点/基本可集成模型的总数。最后，我们讨论了在顶点放松的水平保护以及变形矩阵在可集成模型的空间中不是对角线的情况。
We present an intuitive diagrammatic representation of a new class of integrable $\s$-models. It is shown that to any given diagram corresponds an integrable theory that couples $N$ WZW models with a certain number of each of the following four fundamental integrable models, the PCM, the YB model, both based on a group $G$, the isotropic $\s$-model on the symmetric space $G/H$ and the YB model on the symmetric space $G/H$. To each vertex of a diagram we assign the matrix of one of the aforementioned fundamental integrable theories. Any two vertices may be connected with a number of lines having an orientation and carrying an integer level $k_i$. Each of these lines is associated with an asymmetrically gauged WZW model at an arbitrary level $k_i$. Gauge invariance of the full action is translated to level conservation at the vertices. We also show how to immediately read from the diagrams the corresponding $\s$-model actions. The most generic of these models depends on at least $n^2+1$ parameters, where $n$ is the total number of vertices/fundamental integrable models. Finally, we discuss the case where the level conservation at the vertices is relaxed and the case where the deformation matrix is not diagonal in the space of integrable models.
