Dyon structures in the deconfinement phase of lattice gluodynamics: topological clusters, holonomies and Abelian monopoles

TL;DR

This study investigates the topological structures, specifically dyons and monopoles, in lattice gluodynamics during the deconfinement phase, revealing that light dyon-antidyon pairs dominate the thermal Yang-Mills fields.

Contribution

The paper introduces a cluster analysis method to identify dyon constituents in lattice gauge configurations, highlighting the dominance of light dyon-antidyon pairs in the deconfinement phase.

Findings

Light dyon-antidyon pairs are the main contributors in the deconfinement phase.

Clusters of topological charge densities correspond to dyon constituents.

Support for the dyon interpretation is strengthened by monopole and holonomy analyses.

Abstract

The topological structure of lattice gluodynamics is studied at intermediate resolution scale in the deconfining phase with the help of a cluster analysis. UV filtered topological charge densities are determined from a fixed number of low-lying eigenmodes of the overlap Dirac operator with three types of temporal boundary conditions applied to the valence quark fields. This method usually allows to find all three distinguished (anti)dyon constituents in the gauge field of Kraan-van Baal-Lee-Lu (anti)caloron solutions. The clustering of the three topological charge densities in Monte Carlo generated configurations is then used to mark the positions of anticipated (anti)dyons of the corresponding type. In order to support this interpretation, inside these clusters, we search also for time-like Abelian monopole currents (defined in the maximally Abelian gauge) as well as for local holonomies with at least two approximately degenerated eigenvalues. Our results support the view that light dyon-antidyon pairs - in contrast to the heavy (anti)caloron dyon constituents - contribute dominantly to thermal Yang-Mills fields in the deconfinement phase. This paper is dedicated to the memory of Pierre van Baal and Dmitri Igorevich Diakonov who have influenced our work very much.