Deconfinement phase transition in the SU(3) instanton-dyon ensemble

Abstract

Confinement remains one the most interesting and challenging nonperturbative phenomenon in non-Abelian gauge theories. Recent semiclassical [for $SU(2)$] and lattice (for QCD) studies have suggested that confinement arises from interactions of statistical ensembles of instanton dyons with the Polyakov loop. We extend studies of a semiclassical ensemble of dyons to the $SU(3)$ Yang-Mills theory. We find that such interactions do generate the expected first-order deconfinement phase transition. The properties of the ensemble, including correlations and topological susceptibility, are studied over a range of temperatures above and below ${T}_{c}$. Additionally, the dyon ensemble is studied in the Yang-Mills theory containing an extra trace-deformation term. It is shown that such a term can cause the theory to remain confined and even retain the same topological observables at high temperatures.