A potential setup for perturbative confinement

Abstract

A few years ago, 't Hooft suggested a way to discuss confinement in a perturbative fashion. The original idea was put forward in the Coulomb gauge at tree level. In recent years, the concept of a nonperturbative short distance linear potential also attracted phenomenological attention. Motivated by these observations, we discuss how a perturbative framework, leading to a linear piece in the potential, can be developed in a manifestly gauge and Lorentz invariant manner, which moreover enjoys the property of being renormalizable to all orders. We provide an effective action framework to discuss the dynamical realization of the proposed scenario in Yang-Mills gauge theory.