Recombination of dyons into calorons in SU(2) lattice fields at low temperatures

TL;DR

This paper investigates how calorons in SU(2) lattice gauge theory evolve with temperature, showing a transition from dyonic substructure at finite temperatures to non-dissociated calorons at zero temperature, while maintaining nontrivial holonomy.

Contribution

It demonstrates the temperature-dependent change in the topological structure of calorons, revealing a transition from dyonic substructures to unified calorons with nontrivial holonomy at zero temperature.

Findings

Calorons exhibit dyonic substructure at finite temperature.

At zero temperature, calorons appear as non-dissociated, symmetric lumps.

Polyakov line behavior confirms nontrivial holonomy across temperatures.

Abstract

By cooling of equilibrium lattice fields at finite temperature in SU(2) gauge theory it has been shown that topological objects (calorons) observed on the lattice in the confined phase possess a dyonic substructure which becomes visible under certain circumstances. Here we show that, with decreasing temperature of the equilibrium ensemble, the distribution in the caloron parameter space is modified such that the calorons appear non-dissociated into constituent dyons. Still the calorons have nontrivial holonomy which is demonstrated by the Polyakov line behaviour for these configurations. At vanishing temperature (on a symmetric lattice) topological lumps obtained by cooling possess rotational symmetry in 4D and a characteristic double peak structure of Polyakov lines (defined with respect to temporal and spatial directions) with non-trivial asymptotics.