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Particular deformations of 2-D conformal field theory lead to integrable massive quantum field theories. These can be characterized by the relativistic scattering data. We propose a general scheme for classifying the elastic nondegenerate S-matrix in (1 + 1) dimensions starting from the possible boot-strap processes and the spins of the conserved currents. Their identification with the S-matrix coming from the Toda field theory is analyzed. We discuss both cases of Toda field theory constructed with the simply-laced Dynkin diagrams and the nonsimply-laced ones. We present the results of the perturbative analysis and their geometrical interpretations.

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We study a Feigin-Fuchs construction of conformal field theories based on a G ⊗ G/G coset space, in terms of screened bosons and parafermions. This allows us to get the formula for the conformal dimensions of primary operators. Lists of modular invariant partition functions for the SU(3), SO(5) and G2 Wess-Zumino-Witten models are given. Besides the principal series of diagonal invariants, a complementary series exists for SU(3) and SO(5), which is due to the outer automorphism of the Kac-Moody algebra. Moreover, exceptional solutions appear at levels 5, 9, 21 for SU(3), at levels 3, 7, 12 for SO(5) and at levels 3, 4 for G2. From these modular invariants, those for the corresponding GN ⊗ GL/GN+L models are constructed.

We determine which characters of minimal models factorize into an infinite product like the one of the spin operator in the Ising model. In particular, all characters in the Ising model and in the nonunitary minimal Lee-Yang model factorize. This information is used to determine form factors of descendant operators, especially in the scaling Lee-Yang model.