Dyons near the transition temperature in $SU(3)$ lattice gluodynamics

TL;DR

This study investigates the topological structures, specifically dyons, in $SU(3)$ lattice gluodynamics near the transition temperature, using gradient flow and cluster analysis to identify different dyonic constituents and their behavior across phases.

Contribution

It introduces a method to detect and analyze all three dyonic constituents of KvBLL calorons in $SU(3)$ lattice gluodynamics near the transition temperature.

Findings

Topological charge density becomes visible during overimproved gradient flow.

Different cluster charges correspond to phases: around ±1/3 in confined, higher in deconfined.

Heavy dyons are suppressed as temperature increases.

Abstract

We study the topological structure of $SU(3)$ lattice gluodynamics by cluster analysis. This methodological study is meant as preparation for full QCD. The topological charge density is becoming visible in the process of overimproved gradient flow, which is monitored by means of the the Inverse Participation Ratio (IPR). The flow is stopped at the moment when calorons dissociate into dyons due to the overimproved character of the underlying action. This gives the possibility to simultaneously detect all three dyonic constituents of KvBLL calorons in the gluonic field. The behaviour of the average Polyakov loop under (overimproved) gradient flow could be also (as its value) a diagnostics for the actual phase the configuration is belonging to. Timelike Abelian monopole currents and specific patterns of the local Polyakov loop are correlated with the topological clusters.The spectrum of reconstructed cluster charges $Q_{cl}$ corresponds to the phases. It is scattered around $Q_{cl} \approx \pm 1/3$ in the confined phase, whereas it is $Q_{cl} \approx \pm 0.5 \div 0.7$ for heavy dyons and $|Q_{cl}| < 0.3$ for light dyons in the deconfined phase. Heavy dyons are increasingly suppressed with increasing temperature. The paper is dedicated to the memory of Michael Mueller-Preussker who was a member of our research group for more than twenty years.