Dyonic picture of topological objects in the deconfined phase

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 < Tc as constituents of calorons with maximally nontrivial holonomy.

Fermionic Boundary Conditions and the Finite Temperature Transition of QCD

“…For SU(2) the relation to the angle of the Polyakov loop is just as described above [15]. This suppression effect has been investigated on the lattice [30] and might also explain the decrease of the topological susceptibility above Tc [31]. These ideas certainly should be substantiated further with lattice methods -a task which we leave for future studies.…”

Chiral symmetry breaking/restoration in a dyonic vacuum

“…Note added: After our paper was completed we learned about important study [49] on the lattice, in which some of the tests proposed above were successfully performed. For periodic fermions their near-zero eigenmodes with small eigenvalues are indeed identified with the type-M,M dyons, while for antiperiodic fermions those are indeed related with the type-L,L dyons.…”

Dyons near the transition temperature in lattice QCD

“…was observed by Gattringer et al [17,18] and interpreted in the caloron picture, ignoring other topological features of these configurations. In the case of SU (2) and SU (3) lattice gauge theory it has been seen that this property of mobility (and changing degree of localization) is shared also by a band of near-zero modes of the overlap Dirac operator [19][20][21][22].…”