The dyonic picture of topological objects in the deconfined phase

TL;DR

This paper investigates how the spectral properties of the Dirac operator in SU(2) Yang-Mills theory depend on the Polyakov loop sign, revealing a dyonic structure of topological objects in the deconfined phase.

Contribution

It provides evidence that the spectral differences are explained by the asymmetric presence of dyons and antidyons, linking topological objects to the Polyakov loop in the deconfined phase.

Findings

Spectral gap for positive Polyakov loop with localized modes

High density of delocalized near-zero modes for negative Polyakov loop

Dyon-antidyon asymmetry explains spectral properties

Abstract

In the deconfinement phase of quenched SU(2) Yang-Mills theory the spectrum and localization properties of the eigenmodes of the overlap Dirac operator with antiperiodic boundary conditions are strongly dependent on the sign of the average Polyakov loop, $<L>$. For $<L> > 0$ a gap appears with only few, highly localized topological zero and near-zero modes separated from the rest of the spectrum. Instead of a gap, for $<L> < 0$ a high spectral density of relatively delocalized near-zero modes is observed. In an ensemble of positive $<L>$, the same difference of the spectrum appears under a change of fermionic boundary conditions. We argue that this effect and other properties of near-zero modes can be explained through the asymmetric properties and the different abundance of dyons and antidyons -- topological objects also known to appear, however in a symmetric form, in the confinement phase at $T < T_c$ as constituents of calorons with maximally nontrivial holonomy.