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

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 over-improved gradient flow, which is monitored by means of the inverse participation ratio. The flow is stopped at the moment when calorons dissociate into dyons due to the over-improved character of the underlying action. This gives the possibility to simultaneously detect all three dyonic constituents of KvBLL calorons in the gluonic field. The behavior of the average Polyakov loop (PL) under (over-improved) gradient flow could also serve as a diagnostics for the actual phase the configuration is belonging to. Time-like Abelian monopole currents and specific patterns of the local PL are correlated with the topological clusters. The spectrum of reconstructed cluster charges Qcl corresponds to the phases. It is scattered around Qcl ≈ ±1/3 in the confined phase, whereas it is Qcl ≈ ±(0.5 ÷ 0.7) for heavy dyons and for light dyons in the deconfined phase. We estimate the density of heavy and light dyons at three values of temperature. We find that heavy dyons are increasingly suppressed with increasing temperature. The paper is dedicated to the memory of Michael Müller-Preussker who was a member of our research group for more than twenty years.