We calculate a one loop effective action of SU (2) QCD in the presence of the monopole background, and find a possible connection between the resulting QCD effective action and a generalized Skyrme-Faddeev action of the non-linear sigma model. The result is obtained using the gauge-independent decomposotion of the gauge potential into the topological degrees which describes the non-Abelian monopoles and the local dynamical degrees of the potential, and integrating out all the dynamical degrees of QCD.

We investigate the relationship between colour confinement and topological structures derived from the gauge invariant Abelian (Cho-Duan-Ge) decomposition. This Abelian decomposition is made imposing an isometry on a colour field n which selects the Abelian direction; the principle novelty of our study is that we have defined this field in terms of the eigenvectors of the Wilson Loop. This allows us to establish an equivalence between the path ordered integral of the non-Abelian gauge fields with an integral over an Abelian restricted gauge field which is tractable both theoretically and numerically in lattice QCD. By using Stokes' theorem, we can relate the Wilson Loop in terms of a surface integral over a restricted field strength, and show that the restricted field strength may be dominated by topological structures, which occur when one of the parameters parametrising the colour field n winds itself around a non-analyticity in the colour field. If they exist, these objects will lead to an area law scaling for the Wilson Loop and provide a mechanism for quark confinement. We search for these structures in quenched lattice QCD. We perform the Abelian decomposition, and find that the restricted field strength is dominated by peaks on the lattice. Wilson Loops containing these peaks show a stronger area-Law and thus provide the dominant contribution to the string tension.

We investigate the relationship between colour confinement and the gauge independent Cho-Duan-Ge Abelian decomposition. The decomposition is defined in terms of a colour field n; the principle novelty of our study is that we have used a unique definition of this field in terms of the eigenvectors of the Wilson Loop. This allows us to establish an equivalence between the path-ordered integral of the non-Abelian gauge fields and an integral over an Abelian restricted gauge field which is tractable both theoretically and numerically in lattice QCD. We circumvent path ordering without requiring an additional path integral. By using Stokes' theorem, we can compute the Wilson Loop in terms of a surface integral over a restricted field strength, and show that the restricted field strength may be dominated by certain structures, which occur when one of the quantities parametrising the colour field n winds itself around a non-analyticity in the colour field. If they exist, these structures will lead to an area law scaling for the Wilson Loop and provide a mechanism for quark confinement. Unlike most studies of confinement using the Abelian decomposition, we do not rely on a dual-Meissner effect to create the inter-quark potential.We search for these structures in quenched lattice QCD. We perform the Abelian decomposition, and compare the electric and magnetic fields with the patterns expected theoretically. We find that the restricted field strength is dominated by objects which may be peaks of a single lattice spacing in size or extended string-like lines of electromagnetic flux. The objects are not isolated monopoles, as they generate electric fields in addition to magnetic fields, and the fields are not spherically symmetric, but may be either caused Funded by SCOAP 3 .N. Cundy et al. / Nuclear Physics B 895 (2015) 64-131 65 by a monopole/anti-monopole condensate, some other types of topological objects, or a combination of these. Removing these peaks removes the area law scaling of the string tension, suggesting that they are responsible for confinement.