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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 $θ$ (Dirac) term. The $θ$ 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 $θ$ term wholly accounts for the string tension. We confirm the presence of these monopoles in lattice simulations of SU(2) Yang-Mills theory.