Interacting Ensemble of the Instanton-dyons and Deconfinement Phase Transition in the SU(2) Gauge Theory

TL;DR

This paper investigates how ensembles of interacting instanton-dyons influence the deconfinement phase transition in SU(2) gauge theory, highlighting the role of holonomy and dyon density in confinement.

Contribution

It introduces a numerical simulation approach focusing on the back reaction of dyons on holonomy and confinement, providing new insights into the phase transition mechanism.

Findings

Minimum of free energy shifts towards confinement as temperature decreases.

Dyon density increases with decreasing temperature, affecting holonomy.

Self-consistent ensemble parameters vary systematically with temperature.

Abstract

Instanton-dyons, also known as instanton-monopoles or instanton-quarks, are topological constituents of the instantons at nonzero temperature and holonomy. We perform numerical simulations of the ensemble of interacting dyons for the SU(2) pure gauge theory. Unlike previous studies, we focus on back reaction on the holonomy and the issue of confinement. We calculate the free energy as a function of the holonomy and the dyon densities, using standard Metropolis Monte Carlo and integration over parameter methods. We observe that as the temperature decreases and the dyon density grows, its minimum indeed moves from small holonomy to the value corresponding to confinement. We then report various parameters of the self-consistent ensembles as a function of temperature, and investigate the role of inter-particle correlations.