Coloured loops in 4D and their effective field representation

Gaining insight into ensembles of magnetic configurations which could originate the confining string tension between quarks, constitutes a major concern in current lattice investigations. This interest also applies to a different approach, where gauge models with spontaneous symmetry breaking are constructed to describe the confining string as a smooth vortex solution. In this article, we initially show how to incorporate non-Abelian information into an ensemble of monopoles in 4D, characterized by phenomenological parameters. Next, using some recent techniques developed for polymers, we are able to relate the coloured ensemble with a non-Abelian gauge model. This could offer an interesting perspective in discussing some of the different approaches for describing confinement.