A potential setup for perturbative confinement

TL;DR

This paper explores a gauge-invariant, renormalizable perturbative approach to confinement in Yang-Mills theory, aiming to produce a linear potential consistent with nonperturbative phenomena.

Contribution

It develops a manifestly gauge and Lorentz invariant perturbative framework that can generate a linear potential, advancing the understanding of confinement.

Findings

Proposes a renormalizable perturbative method for confinement.

Demonstrates a linear potential within a gauge-invariant framework.

Provides an effective action approach for Yang-Mills theories.

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.