94 Progress of Theoretical Physics Supplement No. 135, 1999 A-D-E Singularity and the Seiberg-Witten Theory

We study the low-energy effective theory of N = 2 supersymmetric Yang-Mills theory with ADE gauge groups in view of the spectral curves of the periodic Toda lattice and the A-D-E singularity theory. We examine the exact solutions by using the Picard-Fuchs equations for the period integrals of the Seiberg-Witten differential. In particular, we find that the superconformal fixed point in the strong coupling region of the Coulomb branch is characterized by the ADE superpotential. We compute the scaling exponents, which agree with the previous results. Seiberg and Witten showed that the low-energy effective theory of N = 2 su-persymmetric gauge theory in four dimensions is determined by the prepotential, a holomorhic function of the period integrals of the meromorphic one-form (the Seiberg-Witten differential) on a Riemann surface. 1) For a simple Lie group G, i