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

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>N</a:mi></a:mrow></a:math>-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.