David R. Junior

Previously, we proposed an infrared vacuum wave functional for S U ( N ) Yang-Mills theory peaked at thin center vortices and showed that it yields an area law for the Wilson loop. In this work, we use this wave functional to calculate the spatial ’t Hooft loop, for which we find a perimeter law, in accordance with ’t Hooft’s criterion for confinement.

Quantum field theory exhibits rich spatial correlation structures even in the vacuum, where entanglement entropy between regions scales with the area of their shared boundary. While this vacuum structure has been extensively studied, far less is understood about how localized wave packets influence correlations between field values in different spatial regions. In this work, we use the Schrödinger representation to study the Rényi mutual information between complementary spatial regions for a localized wave packet of a free massless scalar field in ( d + 1 ) dimensions. We find that the mutual information in this excited state includes both a vacuum term and an excitation-induced contribution. To obtain quantitative results, we specialize to 1 + 1 dimensions and evaluate the Rényi-2 mutual information between the negative and positive halves of the real line. We find that the excitation generates finite, positive correlations that are maximized when the wave packet sits at the boundary and decreases with its distance from it, at a rate determined by the wave packet’s width. Our findings constitute a contribution toward a more comprehensive understanding of quantum correlations in multiparticle states with nontrivial spatial localization, analyzed within a quantum field-theoretical framework.

Lattice simulations and theoretical analyses consistently identify center vortices and monopoles as key nonperturbative configurations in Yang-Mills theory. In the continuum, the effective representation of mixed oriented and nonoriented center vortices showed that these degrees of freedom generate a confining flux tube with N -ality. Independently, studies of correlation functions reveal an infrared behavior characterized by massivelike scales. In this Letter, field correlators are computed for the first time in a theoretical framework based on center vortices. Using an Abelian-projected vacuum wave functional peaked on the mixed ensemble, we show the emergence of a massivelike gauge-invariant field strength correlator. For this behavior, the nonoriented component in the center-vortex condensate turns out to be essential, as is also the case for producing the correct properties of confining flux tubes.

A scenario to understand the asymptotic properties of confinement between quark probes, based on a 4D mixed ensemble of percolating center-vortex world surfaces and chains, was initially proposed by one of us in a non-Abelian setting. More recently, the same physics was reobtained by means of a Schrödinger wave functional peaked at Abelian-projected configurations, which deals with center-vortex lines and pointlike monopoles in real space. In this work, we formulate the Abelian-projected ensemble and reassess the non-Abelian one within the Weingarten lattice representation for the sum over surfaces. In the phase where world surfaces are stabilized by contact interactions and percolate, lattice gauge fields emerge. This generalizes the Goldstone modes in an Abelian loop condensate to the case where non-Abelian degrees of freedom are present. In this language, the different natural matching properties of elementary center-vortex world surfaces and monopole worldlines can be easily characterized. In the lattice, the Abelian setting also implements the original idea that the mixed ensemble reconciles N -ality with the formation of a confining flux tube. In this picture, center vortices and chains explain why Abelian-projected variables capture this property at asymptotic distances while simultaneously allowing for a “dual superconductor” description of the fundamental string. Common features, differences in the continuum, and perspectives will also be addressed.

Recently, a novel approach to quantize SU(N) Yang-Mills theory was proposed, where the configuration space {A μ } is split into sectors labeled by topological defects, and then the gauge is fixed by a sector dependent condition. As the procedure is local in {A μ }, it could be free from Gribov copies. In this work, we review the renormalizability of sectors labeled by an arbitrary number of elementary center vortices.

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.