A study of center vortices in SU(2) and SU(3) gauge theories a

There are several approaches addressing the problem of understanding the mechanism of color confinement in non-Abelian gauge theories. The most popular share the idea that only a subset of the degrees of freedom are relevant for confinement. In the Abelian projection approach, one takes into account the maximal Abelian subgroup U(1) of the gauge group SU(N) and monopoles are the effective degrees of freedom under study. In the Center projection approach, it is the center group ZN which is considered and center vortices are the effective degrees of freedom under study. These two schemes are commonly believed to give alternative descriptions of confinement. Many analytical and numerical studies have been and are being performed using these two approaches. They give clear evidence that both Abelian and center degrees of freedom play a relevant role. The reduction of the gauge symmetry and the selection of the effective degrees of freedom is usually carried out by a partial fixing of the initial SU(N) gauge freedom. We show that, in the Laplacian Center gauge, monopoles and center vortices are closely related in a unified description and that the latter are the effective degrees of freedom relevant for confinement. Indeed center vortices are related to a more reduced gauge symmetry than monopoles. A fundamental issue of this study is the use of the Laplacian Center gauge, which is free from the problem of the lattice Gribov copies affecting the widely used Maximal Center gauge.