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

We consider N = 1, SU(Nc) gauge theory with an adjoint matter field Φ, Nf flavors of fundamentals Q and antifundamentals Q, and tree-level superpotential of the form QΦlQ. This superpotential is relevant or marginal for lNf ≤ 2Nc. 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 = 1 superconformal fixed points. We discuss them in some detail for Nc = 2, Nf = 1.