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 \tQ, and tree-level superpotential of the form $\tQ\Phi^l Q$. This superpotential is relevant or marginal for $lN_f\leq 2N_c$. 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=1 superconformal fixed points. We discuss them in some detail for N_c=2, N_f=1. 
Anton Kapustin