Complete Monopole Dominance of the Static Quark Potential

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.