论文标题
缝隙 - 条纹ising边界共形场理论1：离散和连续的函数空间
Slit-strip Ising boundary conformal field theory 1: Discrete and continuous function spaces
论文作者
论文摘要
这是一系列文章中的第一篇，以从狭缝 - strip几何形状中关键ISING模型的缩放限制中恢复边界综合场理论（CFT）的完整代数结构。在这里，我们在连续域中介绍了全态函数的空间，以及晶格域中离散全态函数的相应空间。我们发现，在狭缝strip域中的三个无限方向上，其特征在于其奇异行为的特征。我们证明了与连续元的分离式霍明函数的收敛结果。在随后的文章中，离散的全态函数将用于计算ISING模型融合系数（以及ISING转移矩阵的对角线化），并使用函数的收敛来证明融合系数的融合。还将表明，可以通过涉及杰出的连续函数的几何变换从融合系数的极限中恢复边界综合场理论的顶点操作员代数。
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.
