The Coulomb branch of N=1 supersymmetric gauge theory with adjoint and fundamental matter

We consider N = 1 SU(N-c) gauge theory with an adjoint matter field Phi, N-f flavors of fundamentals Q and antifundamentals (Q) over tilde, and tree-level superpotential of the form (Q) over tilde Phi(1)Q. This superpotential is relevant or marginal for lN(f) less than or equal to 2N(c). The theory has a Coulomb branch which is not lifted by quantum corrections. We find the exact effective gauge coupling on the Coulomb branch in terms of a family of hyperelliptic curves, thus providing a generalization of known results about N = 2 SUSY QCD to N = 1 context The Coulomb branch has singular points at which mutually nonlocal dyons become massless. These singularities presumably correspond to new N = I superconformal fixed points. We discuss them in some detail for N-2 = 2, N-f = 1. (C) 1997 Elsevier Science B.V.