ON CLASSIFICATION OF N = 2 SUPERSYMMETRIC THEORIES

We find a relation between the spectrum of solitons of massive N = 2 q uantum field theories in d = 2 and the scaling dimensions of chiral fi elds at the conformal point. The condition that the scaling dimensions be real imposes restrictions on the soliton numbers and leads to a cl assification program for symmetric N = 2 conformal theories and their massive deformations in terms of a suitable generalization of Dynkin d iagrams (which coincides with the A-D-E Dynkin diagrams for minimal mo dels). The Landau-Ginzburg theories are a proper subset of this classi fication. In the particular case of LG theories we relate the soliton numbers with intersection of vanishing cycles of the corresponding sin gularity; the relation between soliton numbers and the scaling dimensi ons in this particular case is a well known application of Picard-Lefs chetz theory.