Local Chirality of Low-Lying Dirac Eigenmodes and the Instanton Liquid Model

TL;DR

This study investigates the local structure of topological charge fluctuations in QCD using low-lying Dirac eigenmodes, revealing discrepancies with the Instanton Liquid Model and suggesting a more complex vacuum structure.

Contribution

It provides new lattice QCD results showing that local topological structures do not align with instanton-based assumptions, challenging existing models of QCD vacuum fluctuations.

Findings

Size and density of local structures disagree with Instanton Liquid Model

Double-peaking behavior is necessary but not sufficient for instanton dominance

Vacuum fluctuations are not dominated by locally quantized lumps

Abstract

The reasons for using low-lying Dirac eigenmodes to probe the local structure of topological charge fluctuations in QCD are discussed, and it is pointed out that the qualitative double-peaked behavior of the local chiral orientation probability distribution in these modes is necessary, but not sufficient for dominance of instanton-like fluctuations. The results with overlap Dirac operator in Wilson gauge backgrounds at lattice spacings ranging from a~0.04 fm to a~0.12 fm are reported, and it is found that the size and density of local structures responsible for double-peaking of the distribution are in disagreement with the assumptions of the Instanton Liquid Model. More generally, our results suggest that vacuum fluctuations of topological charge are not effectively dominated by locally quantized (integer-valued) lumps in QCD.