Confinement, Holonomy and Correlated Instanton-Dyon Ensemble I: SU(2) Yang-Mills Theory

TL;DR

This paper investigates the confinement mechanism in SU(2) Yang-Mills theory through a detailed numerical study of a correlated ensemble of instanton-dyons, emphasizing the role of nontrivial holonomy.

Contribution

It introduces a comprehensive numerical analysis of instanton-dyon ensembles with correlations, highlighting the importance of holonomy in confinement.

Findings

Holonomy influences the confinement phase transition.

Correlated instanton-dyon ensembles reproduce key confinement features.

Numerical results support the dyon-based confinement mechanism.

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 chromo-magnetically 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 (non-supersymmetric) 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.