Confinement, holonomy, and correlated instanton-dyon ensemble: SU(2) Yang-Mills theory

Abstract

The mechanism of confinement in Yang-Mills theories remains a challenge to our understanding of nonperturbative gauge dynamics. While it is widely perceived that confinement may arise from chromomagnetically charged gauge configurations with nontrivial topology, it is not clear what types of configurations could do that and how, in pure Yang-Mills and QCD-like (nonsupersymmetric) theories. Recently, a promising approach has emerged, based on statistical ensembles of dyons/anti-dyons that are constituents of instanton/anti-instanton solutions with nontrivial holonomy where the holonomy plays a vital role as an effective ``Higgsing'' mechanism. We report a thorough numerical investigation of the confinement dynamics in $SU(2)$ Yang-Mills theory by constructing such a statistical ensemble of correlated instanton-dyons.