On Different Criteria for Confinement

Abstract

We compare two approaches in supersymmetric confinement, the Seiberg formulation and the superconvergence rule. For the latter, the critical point is $\gamma_{00}=0$ in the Landau gauge. We find $4\gamma_{00}=\beta_0$ is the critical point for most of confining theories without a tree-level superpotential in the Seiberg formulation, in particular, in the large $N_c$ and $N_f$ limit. We show how confining theories with a discrete symmetry and a tree-level superpotential connect these two critical points: the large and small discrete symmetry limits correspond to the critical points $4\gamma_{00}=\beta_0$ and $\gamma_{00}=0$, respectively.