On Classification of N=2 Supersymmetric Theories, (e-mail uncorrupted version)

Details On Classification of N=2 Supersymmetric Theories, (e-mail uncorrupted version) On Classification of N=2 Supersymmetric Theories, (e-mail uncorrupted version)

1992-11-23

arxiv.org/abs/hep-th/9211097v2

Commun.Math.Phys. 158 (1993) 569-644

Physics

High Energy Physics

High Energy Physics - Theory

116 pages, HUTP-92/A064 and SISSA-203/92/EP

Scientific paper

10.1007/BF02096804

We find a relation between the spectrum of solitons of massive $N=2$ quantum field theories in $d=2$ and the scaling dimensions of chiral fields at the conformal point. The condition that the scaling dimensions be real imposes restrictions on the soliton numbers and leads to a classification program for symmetric $N=2$ conformal theories and their massive deformations in terms of a suitable generalization of Dynkin diagrams (which coincides with the A--D--E Dynkin diagrams for minimal models). The Landau-Ginzburg theories are a proper subset of this classification. In the particular case of LG theories we relate the soliton numbers with intersection of vanishing cycles of the corresponding singularity; the relation between soliton numbers and the scaling dimensions in this particular case is a well known application of Picard-Lefschetz theory.

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