Confinement by Monopole Loops in Inhomogeneous Magnetic Field

TL;DR

This paper demonstrates that in a non-uniform magnetic field, a generalized Polyakov mechanism can induce confinement in 3+1 dimensions at weak coupling, with monopole loops playing a crucial role depending on the field's properties.

Contribution

It extends the Polyakov confinement mechanism to inhomogeneous magnetic fields in 3+1 dimensions, revealing conditions under which monopole loops lead to confinement.

Findings

Confinement occurs in 3+1 dimensions with inhomogeneous magnetic fields.

Monopole loops develop an almost flat direction at the threshold.

The mechanism resembles the 2+1 dimensional Polyakov confinement process.

Abstract

We show that a generalized Polyakov mechanism can lead to confinement at weak coupling in $3+1$ dimensions when the theory is placed in a non-trivial, spatially varying magnetic field background. Depending on the magnitude of the field and the length scale of its spatial variation, the "dual" Schwinger mechanism for monopole-antimonopole pair creation may or may not be operative. At the threshold, monopole loops in the Euclidean description develop an almost flat direction. In this regime, confinement arises in a way similar to the $2+1$ dimensional Polyakov mechanism and the monopoles and antimonopoles are effectively replaced by deconfined "bits" of a monopole loop.