Complete Monopole Dominance of the Static Quark Potential

TL;DR

This paper demonstrates that monopoles are solely responsible for the static quark potential in SU(2) Yang-Mills theory, using gauge-independent Abelian decomposition and lattice simulations to isolate topological confinement mechanisms.

Contribution

It introduces a gauge-independent method to identify monopoles responsible for confinement, confirming their dominance in the static quark potential through theoretical analysis and lattice simulations.

Findings

Monopoles fully account for the string tension in the static quark potential.

The Abelian decomposition isolates topological objects responsible for confinement.

Lattice simulations confirm the monopole dominance in SU(2) Yang-Mills theory.

Abstract

In earlier work, we used a gauge independent Abelian Decomposition to show that Abelian degrees of freedom are wholly responsible for the static quark potential. The restricted Abelian field can be split into two terms, a Maxwell term and a $\theta$ (Dirac) term. The $\theta$ term's contribution to the string tension can be analysed theoretically and numerically, and arises because of the existence of a certain type of monopole. While the Abelian field can be constructed without gauge fixing, its two component parts are gauge-dependent, with a gauge transformation moving the topological features from one part to another. This allows us to isolate and identify the topological objects responsible for confinement by constructing a gauge where the $\theta$ term wholly accounts for the string tension. We confirm the presence of these monopoles in lattice simulations of SU(2) Yang-Mills theory.