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

The dyonic picture of topological objects in the deconfined phase