We show that four-dimensional N = 2 supersymmetric SU (N ) gauge theory for N > 2 necessarily contains vacua with mutually non-local massless dyons, using only analyticity of the effective action and the weak coupling limit of the moduli space of vacua. A specific example is the Z 3 point in the exact solution for SU (3), and we study its effective Lagrangian. We propose that the low-energy theory at this point is an N = 2 superconformal U (1) gauge theory containing both electrically and magnetically charged massless hypermultiplets.

New examples of N =2 supersymmetric conformal field theories are found as fixed points of SU (2) N =2 supersymmetric QCD. Relations among the scaling dimensions of their relevant chiral operators, global symmetries, and Higgs branches are understood in terms of the general structure of relevant deformations of non-trivial N =2 conformal field theories. The spectrum of scaling dimensions found are all those compatible with relevant deformations of a y 2 = x 3 singular curve.

We analyze in detail the moduli space of vacua of N =2 SUSY QCD with n c colors and n f flavors. The Coulomb branch has submanifolds with non-Abelian gauge symmetry.The massless quarks and gluons at these vacua are smoothly connected to the underlying elementary quarks and gluons. Upon breaking N =2 by an N =1 preserving mass term for the adjoint field the theory flows to N =1 SUSY QCD. Some of the massless quarks and gluons on the moduli space of the N =2 theory become the magnetic quarks and gluons of the N =1 theory. In this way we derive the duality in N =1 SUSY QCD by identifying its crucial building blocks-the magnetic degrees of freedom-using only semiclassical physics and the non-renormalization theorem. 3/96

We present an exact description of the metric on the moduli space of vacua and the spectrum of massive states for four dimensional N = 2 supersymmetric SU(n) gauge theories. The moduli space of quantum vacua is identified with the moduli space of a special set of genus n -1 hyperelliptic Riemann surfaces.

We present an explicit non-perturbative solution of N =2 supersymmetric SU (N ) gauge theory with N f ≤ 2N flavors generalizing results of Seiberg and Witten for N = 2.