标题： 狭缝条带伊辛边界共形场理论 2：融合系数的标度极限 显示英文标题

标题： Slit-strip Ising boundary conformal field theory 2: Scaling limits of fusion coefficients

摘要： 这是关于从狭缝条形几何中临界伊辛模型的标度极限恢复边界共形场论（CFT）的完整代数结构的三篇文章中的第二篇。 在这里，我们研究具有局部单色边界条件的格点狭缝条形伊辛模型的融合系数。 融合系数是截断格点狭缝条形在三个端点处的边界相关函数的某些归一化极限，在一个相关函数本质上随截断高度呈指数依赖性的随机变量基底下。 关键技巧是将某些离散解析函数与取值为算子的离散1-形式相关联。 这与边界共形场论中的电流有直接类比。 对于该技巧的两个具体应用，我们使用了系列第一篇文章中的特殊离散解析函数。 首先，我们以一种与边界共形场论相平行的形式重新推导出伊辛转移矩阵的对角化。 其次，我们通过仅用特殊离散解析函数的内积表示的递归关系来表征伊辛模型的融合系数。 然后可以利用第一部分证明的离散解析函数的收敛结果，推导出在标度极限下融合系数的收敛性。 在系列的第三篇文章中，将展示在考虑我们选择的狭缝条形几何的变换之后，融合系数的标度极限将成为费米型共形场论的顶点算子代数的结构常数。 显示英文摘要

摘要： This is the second in a series of three articles about recovering the full algebraic structure of a boundary conformal field theory (CFT) from the scaling limit of the critical Ising model in slit-strip geometry. Here we study the fusion coefficients of the Ising model in the lattice slit-strip, with locally monochromatic boundary conditions. The fusion coefficients are certain renormalized limits of boundary correlation functions at the three extremities of the truncated lattice slit-strips, in a basis of random variables whose correlation functions have an essentially exponential dependence on the truncation heights. The key technique is to associate operator valued discrete 1-forms to certain discrete holomorphic functions. This provides a direct analogy with currents in boundary conformal field theory. For two specific applications of this technique, we use distinguished discrete holomorphic functions from the first article of the series. First, we rederive the known diagonalization of the Ising transfer matrix in a form that parallels boundary conformal field theory. Second, we characterize the Ising model fusion coefficients by a recursion written purely in terms of inner products of the distinguished discrete holomorphic functions. The convergence result for the discrete holomorphic functions proven in the first part can then be used to derive the convergence of the fusion coefficients in the scaling limit. In the third article of the series, it will be shown that up to a transformation that accounts for our chosen slit-strip geometry, the scaling limits of the fusion coefficients become the structure constants of the vertex operator algebra of a fermionic conformal field theory.