From Center-Vortex Ensembles to the Confining Flux Tube

Abstract

In this review, we discuss the present status of the description of confining flux tubes in SU(N) pure Yang–Mills theory in terms of ensembles of percolating center vortices. This is based on three main pillars: modeling in the continuum the ensemble components detected in the lattice, the derivation of effective field representations, and contrasting the associated properties with Monte Carlo lattice results. The integration of the present knowledge about these points is essential to get closer to a unified physical picture for confinement. Here, we shall emphasize the last advances, which point to the importance of including the non-oriented center-vortex component and non-Abelian degrees of freedom when modeling the center-vortex ensemble measure. These inputs are responsible for the emergence of topological solitons and the possibility of accommodating the asymptotic scaling properties of the confining string tension.

The infrared Yang-Mills wave functional due to percolating center vortices

“…We found an area law for the Wilson loop and a string tension that shows an asymptotic Casimir scaling, which is in line with one of the possible scalings seen in lattice calculations. These properties agree with those found in the 4d ensemble of percolating centervortex surfaces with oriented and non-oriented components (for a review, see [10]). The results obtained in this work provide further evidence that the coexistence of these components, together with their natural correlations, are essential to describe all the asymptotic confining properties in Yang-Mills theory.…”

“…[5], and also found on the lattice [39], non-oriented center vortices are absolutely necessary for a non-vanishing Pontryagin index. Furthermore, in 4d ensembles of percolating center vortices, the coexistence of oriented and non-oriented components, N -matching rules among center-vortex surfaces, and natural matching rules among monopole lines, is essential to generate a confining flux tube [9] (see also [10]). Indeed, the center-vortex field configurations in our vacuum wave functional incorporate all the features and correlations of center vortices observed for SU (2) in the indirect maximal center gauge, naturally extended to SU (N ).…”

“…In Ref. [9] (see also [10]), it was argued that ensembles of percolating oriented and non-oriented center-vortex surfaces together with natural correlations could generate, besides N -ality, the confining flux tube between quarks [11][12][13][14] and the Lüscher term [15]. The line of reasoning is as follows.…”

Renormalizability of a first principles Yang-Mills center-vortex ensemble

“…This points to the idea that Singer's no go theorem is the fundamental reason behind a first-principles YM center-vortex ensemble. Furthermore, this could establish a connection with phenomenological ensembles of center vortices, which are known to successfully reproduce the properties of the confining string (see the reviews [35,36], and references therein).…”

Modern Approaches to Non-Perturbative QCD and Other Confining Gauge Theories

“…The related review [9] by Luis Esteban Oxman and his collaborators provides an overview of the recent progress achieved by the authors in an analytic derivation of the center-vortex model of the Yang-Mills vacuum. This research program starts with modeling, in the continuum limit, of some of the properties of center vortices that were found in the lattice simulations, and proceeds toward the derivation of the corresponding effective field representations.…”