$N=2$ Superconformal Field Theories in $4$ Dimensions and A-D-E Classification

Abstract

Making use of the exact solutions of the $N=2$ supersymmetric gauge theories we construct new classes of superconformal field theories (SCFTs) by fine-tuning the moduli parameters and bringing the theories to critical points. In the case of SCFTs constructed from pure gauge theories without matter $N=2$ critical points seem to be classified according to the A-D-E classification as in the two-dimensional SCFTs.

19 pages LaTeX; Talk given by T. Eguchi at "Mathematical Beauty of Physics in Memory of Claude Itzykson", Saclay, June 5-7, 1996