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

Taha Ameen, Kalle Kytölä*, S. C. Park, David Radnell

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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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, and note in particular that natural subsets of these functions span analogues of Hardy spaces. 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.

Original languageEnglish
Article number30
Pages (from-to)1-53
Number of pages53
JournalMathematical Physics Analysis and Geometry
Issue number4
Publication statusPublished - Dec 2022
MoE publication typeA1 Journal article-refereed


  • Conformal field theory
  • Discrete complex analysis
  • Ising model


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