Even before the introduction of Conformal Field Theory by Belavin, Polyakov and Zamolodchikov, many exponents and dimensions of 2D lattice models at criticality were derived by den Nijs and Nienhuis using Coulomb gas techniques. The latter postulate (unrigorously) that height functions of lattice models converge to the Gaussian Free Field, which is in many ways mysterious, in particular was never formulated in the presence of a boundary. We will discuss possible formulations and their relations to CFT, SLE and conformal invariance of critical lattice models.
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