Abstract
The connection between Rational Conformal Field Theory (RCFT), N = 2 massive supersymmetric field theory, and solvable Interaction Round the Face (IRF) lattice models is explored here. Specifically, one identifies the fusion rings with the chiral rings. The theories so obtained are conjectured, and largely shown, to be integrable, based on a variety of examples, and the structure of the metric in moduli space. The kink scattering theory is given by the Boltzman weights of an IRF model, which is built entirely in terms of the conformal data of the original RCFT. This procedure produces all solvable IRF models in terms of projection operators of the RCFT. The soliton structure and their scattering amplitudes are described. A host of new RCFT are described in a way which generalizes much, if not all, of the known ones.
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