A New visita to the SU(N) gauge field confinement

TL;DR

This paper introduces an exact effective spin model to study $SU(N)$ gauge field confinement at zero temperature, revealing that the Polyakov and Wilson potentials are identical, and enabling confinement analysis in the continuum limit.

Contribution

It presents a novel approach using an effective spin model to analyze $SU(N)$ confinement via the Wilson line, differing from traditional potential-based methods.

Findings

Confirmed confinement in $SU(2)$ with a linear Polyakov potential

Demonstrated the equivalence of Polyakov and Wilson potentials

Enabled study of confinement in the continuum limit

Abstract

Based on our exact effective spin model, the zero temperature $SU(N)$ gauge field confinement has been studied by the deconfinement-confinement phase transition order parameter, i.e. the Wilson line, rather than the quark antiquark potential. The procedure would allow one to study the confinement in the true continuum limit. For the $(1+1)$ $SU(2)$ gauge field, the confinement and a linear zero temperature Polyakov quark antiquark potential were shown. It is also shown, for the first time, that the Polyakov and Wilson potentials are identical.