On Different Criteria for Confinement

TL;DR

This paper compares two criteria for supersymmetric confinement, analyzing their critical points and how they relate in theories with discrete symmetries and superpotentials, providing insights into the conditions for confinement.

Contribution

It identifies and compares the critical points of two confinement criteria in supersymmetric theories and explores their connection through symmetry and superpotential considerations.

Findings

Critical point for superconvergence: $eta_0/4$

Critical point for Seiberg formulation: $eta_0/4$ in large $N_c$, $N_f$ limit

Connection between criteria via symmetry limits

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.