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

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 Lüscher 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.

arXiv commentLaTeX, 17 pages, 3 figures

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Cited by in corpus (7)

• Unifying Monopole and Center Vortex as the Semiclassical Confinement Mechanism
• Different faces of confinement
• From center-vortex ensembles to the confining flux tube
• The infrared Yang-Mills wave functional due to percolating center vortices
• Ensembles of center vortices and chains: Insights from a natural lattice framework
• Study of Gribov Copies in the Yang-Mills ensemble
• Hints of (de)confinement in Yang-Mills-Chern-Simons theories in the maximal Abelian gauge