On the topological content of SU(2) gauge fields below T_c

TL;DR

This study investigates the topological structures of SU(2) gauge fields near the confinement-deconfinement transition, identifying calorons and dyons, and linking lattice configurations to semi-classical solutions with non-trivial holonomy.

Contribution

It provides a detailed analysis of topological excitations in finite-temperature SU(2) gauge fields, connecting lattice results with Kraan-van Baal solutions and highlighting the role of dyons and holonomy.

Findings

Calorons with unit topological charge are observed.

Dyon pairs are identified and described by analytic solutions.

Configurations are consistent with semi-classical Kraan-van Baal solutions.

Abstract

Finite temperature Euclidean 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 non-integer) topological charge. Two kinds of spatial boundary conditions (fixed holonomy and standard periodic boundary conditions) are applied. For the lowest-action almost-classical 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-)selfdual lumps (BPS-monopoles or dyons) combined in pairs of non-integer (equal or opposite sign) topological charge. For calorons and separated pairs of equal-sign dyons obtained by cooling we have found that (i) the gluon field is well-described by Kraan-van Baal solutions of the Euclidean Yang-Mills field equations and (ii) the lowest Wilson-fermion modes are well-described by analytic solutions of the corresponding Dirac equation. For metastable configurations found at higher action, the multi-center structure can be interpreted in terms of dyons and antidyons, using the gluonic and fermionic indicators as in the dyon-pair case. Additionally, the Abelian monopole structure and field strength correlators between the centers are useful to analyse the configurations in terms of dyonic constituents. We argue that a semi-classical approximation of the non-zero temperature path integral should be built on superpositions of solutions with non-trivial holonomy.