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 a 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.