The dyonic picture of topological objects in the deconfined phase

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.