Calorons, instantons and constituent monopoles in SU(3) lattice gauge theory

TL;DR

This paper investigates the localization of Dirac zero-modes in SU(3) lattice gauge theory at finite temperature, revealing structured excitations consistent with Kraan-van Baal solutions involving constituent monopoles.

Contribution

It provides the first detailed comparison of zero-mode localization under different boundary conditions, supporting the presence of constituent monopoles in the QCD vacuum.

Findings

Zero-modes localize differently with boundary conditions

Results align with Kraan-van Baal monopole solutions

Vacuum excitations are more complex than instantons

Abstract

We analyze the zero-modes of the Dirac operator in quenched SU(3) gauge configurations at non-zero temperature and compare periodic and anti-periodic temporal boundary conditions for the fermions. It is demonstrated that for the different boundary conditions often the modes are localized at different space-time points and have different sizes. Our observations are consistent with patterns expected for Kraan - van Baal solutions of the classical Yang-Mills equations. These solutions consist of constituent monopoles and the zero-modes are localized on different constituents for different boundary conditions. Our findings indicate that the excitations of the QCD vacuum are more structured than simple instanton-like lumps.