Coloured loops in 4D and their effective field representation
  Gaining insight about ensembles of magnetic configurations, that 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 were able to relate the coloured ensemble with a non Abelian gauge model. This could offer an interesting perspective to discuss some of the different approaches to describe confinement. 
L. E. Oxman, G. C. Santos Rosa, B. F. I. Teixeira
hep-th math-ph math.MP