Searching for KvBLL calorons in SU(3) lattice gauge field ensembles

TL;DR

This paper investigates KvBLL caloron solutions in SU(3) lattice gauge theory, identifying their signatures through lattice discretization, cooling, and analysis of zero modes and topological charge density.

Contribution

It introduces lattice versions of KvBLL solutions and demonstrates their presence in finite temperature SU(3) ensembles using multiple analysis techniques.

Findings

Clear evidence of KvBLL-like backgrounds in lattice ensembles.

Identification of dyonic structures via cooling and topological charge density.

Correlation of zero modes with KvBLL solutions.

Abstract

We discuss Kraan - van Baal - Lee - Lu (KvBLL) solutions of the classical Yang-Mills equations with temperature in the context of SU(3) lattice gauge theory. We present discretized lattice versions of KvBLL solutions and other dyonic structures, obtained by cooling in order to understand their variety and signature. An analysis of the zero modes of the lattice Dirac operator for different fermionic boundary conditions gives clear evidence for a KvBLL-like background of finite T lattice subensembles with Q = +/-1. Using APE-smearing we are able to study the topological charge density q(x) of the configurations and to corroborate this interpretation.