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Abstract
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 slitstrip 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 slitstrip 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 language  English 

Article number  30 
Pages (fromto)  153 
Number of pages  53 
Journal  Mathematical Physics Analysis and Geometry 
Volume  25 
Issue number  4 
DOIs  
Publication status  Published  Dec 2022 
MoE publication type  A1 Journal articlerefereed 
Keywords
 Conformal field theory
 Discrete complex analysis
 Ising model
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FiRST Kytölä: Finnish centre of excellence in Randomness and STructures (FiRST)
Kytölä, K., Adame Carrillo, D. & Behzad, D.
01/01/2022 → 31/12/2024
Project: Academy of Finland: Other research funding