3D Yang-Mills confining properties from a non-Abelian ensemble perspective

TL;DR

This paper develops a non-Abelian ensemble measure for 3D center-vortex configurations, deriving an effective field theory that explains confinement and string tension scaling consistent with Monte Carlo results.

Contribution

It introduces a novel non-Abelian ensemble framework for 3D Yang-Mills theory, linking vortex dynamics to confinement and Casimir scaling.

Findings

Reproduces confinement features observed in Monte Carlo simulations.

Shows string tension scales with the quadratic Casimir of quark representations.

Predicts stable domain walls between quarks supporting a linear potential.

Abstract

In this work, we propose a $3D$ ensemble measure for center-vortex worldlines and chains equipped with non-Abelian degrees of freedom. We derive an effective field description for the center-element average where the vortices get represented by $N$ flavors of effective Higgs fields transforming in the fundamental representation. This field content is required to accommodate fusion rules where $N$ vortices can be created out of the vacuum. The inclusion of the chain sector, formed by center-vortex worldlines attached to pointlike defects, leads to a discrete set of $Z(N)$ vacua. This type of SSB pattern supports the formation of a stable domain wall between quarks, thus accommodating not only a linear potential but also the L\"uscher term. Moreover, after a detailed analysis of the associated field equations, the asymptotic string tension turns out to scale with the quadratic Casimir of the antisymmetric quark representation. These behaviors reproduce those derived from Monte Carlo simulations in $SU(N)$ $3D$ Yang-Mills theory, which lacked understanding in the framework of confinement as due to percolating magnetic defects.