Ensembles of center vortices and chains: Insights from a natural lattice framework

TL;DR

This paper explores the role of center vortices and chains in confinement using a lattice framework, connecting Abelian and non-Abelian perspectives to understand flux tube formation and confinement mechanisms.

Contribution

It formulates the Abelian-projected ensemble within the Weingarten lattice representation, bridging Abelian and non-Abelian confinement descriptions and characterizing vortex and monopole configurations.

Findings

Lattice gauge fields emerge in the percolating phase of worldsurfaces.

Center vortices and chains explain N-ality and flux tube formation.

The Abelian setting captures confinement properties at large distances.

Abstract

A scenario to understand the asymptotic properties of confinement between quark probes, based on a 4D mixed ensemble of percolating center-vortex worldsurfaces 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 Schr\"odinger wavefunctional 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 worldsurfaces 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 worldsurfaces 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.