Calorons and dyons at the thermal phase transition analyzed by overlap fermions

TL;DR

This study uses overlap fermions and topological charge density to identify calorons and dyons in SU(2) gauge theory at the deconfinement transition, revealing their profiles and boundary condition dependencies.

Contribution

It demonstrates a method to classify topological lumps as calorons or dyons using eigenmodes of the overlap Dirac operator with boundary conditions, at the phase transition.

Findings

Lumps can be classified as calorons or dyons based on boundary conditions.

Polyakov loop profiles inside clusters match caloron/dyon characteristics.

The method is effective at the deconfinement transition on improved lattice actions.

Abstract

In a pilot study, we use the topological charge density defined by the eigenmodes of the overlap Dirac operator (with ultraviolet filtering by mode-truncation) to search for lumps of topological charge in SU(2) pure gauge theory. Augmenting this search with periodic and antiperiodic temporal boundary conditions for the overlap fermions, we demonstrate that the lumps can be classified either as calorons or as separate caloron constituents (dyons). Inside the topological charge clusters the (smeared) Polyakov loop is found to show the typical profile characteristic for calorons and dyons. This investigation, motivated by recent caloron/dyon model studies, is performed at the deconfinement phase transition for SU(2) gluodynamics on 20^3 x 6 lattices described by the tadpole improved L\"uscher-Weisz action. The transition point has been carefully located. As a necessary condition for the caloron/dyon detection capability, we check that the LW action, in contrast to the Wilson action, generates lattice ensembles, for which the overlap Dirac eigenvalue spectrum smoothly behaves under smearing and under the change of the boundary conditions.