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We review the algebraic and analytic aspects of the conformal field theory (CFT) and its relation to the stochastic Loewner evolution (SLE) in an example of the Ising model. We obtain the scaling limit of the correlation functions of Ising free fermions on an arbitrary simply connected two-dimensional domain D. Then, we study the analytic and algebraic aspects of the fermionic CFT on D, using the Fock space formalism of fields, and the Clifford vertex operator algebra (VOA). These constructionsarXiv:1505.01405v1 fatcat:m6duwzkisjgu3me5dr72yw22k4