Topological content ofSU(2)gauge fields belowTc

Abstract

Finite temperature Euclidean $\mathrm{SU}(2)$ lattice gauge fields generated in the confinement phase close to the deconfinement phase transition are subjected to cooling. The aim is to identify long-living, almost-classical local excitations which carry (generically noninteger) topological charge. Two kinds of spatial boundary conditions (fixed holonomy and standard periodic boundary conditions) are applied. For the lowest-action configurations we find that their relative probability semi-quantitatively agrees for both types of boundary conditions. We find calorons with unit topological charge as well as (anti-)self-dual lumps of noninteger (equal or opposite sign) topological charge (Bogomol'nyi-Prasad-Sommerfield monopoles or dyons) combined in pairs. For calorons and separated pairs of equal-sign dyons we have found (i) the gluon field to be well-described by Kraan--van Baal solutions of the field equations and (ii) the real Wilson-fermion modes to be well approximated by analytic solutions of the corresponding Dirac equation. For metastable configurations found at higher action, the multicenter structure can also be interpreted in terms of dyons and antidyons, using the gluonic and fermionic indicators as for the dyon-pair case. We argue that an improvement of the semiclassical caloron approach to the nonzero temperature path integral should take into account superpositions of solutions with nontrivial holonomy.