What Are We Learning from 2 - Dimensional Conformal Models ? * )

Rational conformal field theories are reviewed from an (informal) axiomatic stand point. This approach sheds new light on the classification of conformal current algebra models. On the other hand, the study of 2D CFT gives rise to new questions in the general theory. We display as an example embeddings of local chiral algebras which are not of the Doplicher–Haag–Roberts type. The interrelation between this branch of mathematical physics and some problems of pure mathematics is emphasized