Topological Structure of the QCD Vacuum Revealed by Overlap Fermions

TL;DR

This paper uses overlap fermions to explore the topological structure of the QCD vacuum, revealing how spectral filtering affects charge distribution and eigenmode localization, supporting instanton-like features.

Contribution

It demonstrates the impact of spectral cut-offs on topological charge density and eigenmode localization, linking lattice results to continuum instanton models.

Findings

Charge density structure varies with spectral cut-off.

UV filtering reveals instanton-like topological features.

Eigenmodes are highly localized and chiral.

Abstract

Overlap fermions preserve a remnant of chiral symmetry on the lattice. They are a powerful tool to investigate the topological structure of the vacuum of Yang-Mills theory and full QCD. Recent results concerning the localization of topological charge and the localization and local chirality of the overlap eigenmodes are reported. The charge distribution is radically different, if a spectral cut-off for the Dirac eigenmodes is applied. The density q(x) is changing from the scale-a charge density (with full lattice resolution) to the ultraviolet filtered charge density. The scale-a density, computed on the Linux cluster of LRZ, has a singular, sign-coherent global structure of co-dimension 1 first described by the Kentucky group. We stress, however, the cluster properties of the UV filtered topological density resembling the instanton picture. The spectral cut-off can be mapped to a bosonic smearing procedure. The UV filtered field strength reveals a high degree of (anti)selfduality at "hot spots" of the action. The fermionic eigenmodes show a high degree of local chirality. The lowest modes are seen to be localized in low-dimensional space-time regions.