Unifying Monopole and Center Vortex as the Semiclassical Confinement Mechanism

TL;DR

This paper unifies two semiclassical mechanisms, monopoles and center vortices, as explanations for color confinement in 4D Yang-Mills theory by establishing their explicit relation under different compactified setups.

Contribution

It demonstrates the explicit connection between monopole and center vortex mechanisms, unifying them as a single semiclassical confinement explanation.

Findings

Monopole mechanism on a0a0a0 with double-trace deformation.

Center vortex mechanism on a0a0a0 with 't Hooft flux.

Explicit relation established between monopole and vortex descriptions.

Abstract

Magnetic excitations play a crucial role in understanding the color confinement of $4$d Yang-Mills theory, and we have the monopole and the center vortex as plausible candidates to explain its mechanism. Under suitable compactified setups of $4$d Yang-Mills theory, we can achieve different weakly-coupled descriptions of confinement phenomena: The monopole mechanism takes place on $\mathbb{R}^3\times S^1$ with the double-trace deformation, and the center-vortex mechanism is effective on $\mathbb{R}^2\times T^2$ with the 't Hooft flux. We unify these two semiclassical descriptions by showing the explicit relation between the monopole and center vortex.