Coloured loops in 4D and their effective field representation

Abstract

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.

4D ensembles of percolating center vortices and monopole defects: The emergence of flux tubes withN-ality and gluon confinement

“…This is in contrast to the situation in Ref. [61] where an ensemble formed by loops carrying internal degrees in a linear space parametrized by any set of complex numbers z C , C ¼ 1; …; N 2 − 1 was analyzed. These variables label coherent states in an infinite dimensional space of color states [87].…”

“…The weak dependence on these directions allows us to consistently solve the equations by keeping the smaller angular momenta (see Refs. [61,86] Qðx; u; x 0 ; u 0 ; LÞ ≈ Q 0 ðx; x 0 ; LÞ;…”

“…This idea was further elaborated in Ref. [61], where we applied polymer techniques to an ensemble of worldlines with non-Abelian degrees of freedom (d.o.f. )…”

From Center-Vortex Ensembles to the Confining Flux Tube

“…which corresponds to tension µ and stiffness 1/κ. These objects were extensively studied in [46,77]. In what follows, we review the results obtained.…”

SU(N) → Z(N) dual superconductor models: the magnetic loop ensemble point of view

“…Similarly to the dual description of valence gluons, the monopole component in 3 For SU(2), weights are one-component. The fundamental ones are ±w, w = [37]. We also clarify some points regarding the projection over a reduced sector of well-defined color states.…”