缝-条伊辛边界共形场论1：离散和连续函数空间
Slit-strip Ising boundary conformal field theory 1: Discrete and continuous function spaces
摘要：
这是第一次在一系列的文章恢复完整的代数结构的边界共形场论（CFT）的临界伊辛模型的尺度限制在狭缝-条带几何。在这里，我们引入了连续域上的全纯函数空间以及格域上的离散全纯函数空间。我们发现区别的功能，其特点是在三个无限方向上的裂缝带域的奇异行为。证明了离散全纯函数收敛于连续函数的结果。在后续的文章中，离散全纯函数将用于计算伊辛模型融合系数（以及用于伊辛传递矩阵的对角化），并且函数的收敛性用于证明融合系数的收敛性。还将表明，边界共形场论的顶点算子代数可以通过涉及特殊连续函数的几何变换从融合系数的极限恢复。
英文摘要：
This is the first in a series of 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 introduce spaces of holomorphic functions in continuum domains as well as corresponding spaces of discrete holomorphic functions in lattice domains. We find distinguished sets of functions characterized by their singular behavior in the three infinite directions in the slit-strip domains. We prove convergence results of the distinguished discrete holomorphic functions to the continuum ones. In the subsequent articles, the discrete holomorphic functions will be used for the calculation of the Ising model fusion coefficients (as well as for the diagonalization of the Ising transfer matrix), and the convergence of the functions is used to prove the convergence of the fusion coefficients. It will also be shown that the vertex operator algebra of the boundary conformal field theory can be recovered from the limit of the fusion coefficients via geometric transformations involving the distinguished continuum functions.
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