Slit-Strip Ising Boundary Conformal Field Theory 1: Discrete and Continuous Function Spaces

Abstract This is the first in a series of articles about recovering full algebraic structure boundary conformal field theory (CFT) from scaling limit critical Ising model slit-strip geometry. Here, we introduce spaces holomorphic functions continuum domains as well corresponding discrete lattice domains. We find distinguished sets characterized by their singular behavior three infinite directions domains, and note particular that natural subsets these span analogues Hardy spaces. prove convergence results to ones. In subsequent articles, will be used for calculation fusion coefficients (as diagonalization transfer matrix), coefficients. It also shown vertex operator algebra can recovered via geometric transformations involving functions.