A common approach while considering confinement is to study the dominance of
an Abelian subgroup of the SU(3) gauge Links. A good way to find the Abelian
component of the field is through the Cho-Guan-De gauge invariant Abelian
Decomposition, which uses a carefully chosen direction vector n to split the
gauge field into an Abelian restricted field and a remnant coloured field. The
restricted field can be further subdivided into topological and non-topological
terms. We show that there is a choice of n which allows us to exactly
represent the Wilson Loop of full QCD as a function of only the restricted
Abelian field without requiring any path ordering or additional path integrals.
We present numerical evidence showing that the topological part of the
restricted field dominates the string tension. We also show that n contains
certain topological objects, which, if they exist, will be at least partially
responsible for confinement. These leave distinctive patterns in the restricted
field strength, and we search for these structures in quenched lattice QCD.Comment: Lattice 2013 (Vacuum structure), Mainz, July 2013; 7 page