Topological Charge Fluctuations and Low-Lying Dirac Eigenmodes

TL;DR

This paper investigates topological charge fluctuations in QCD using low-lying Dirac eigenmodes, revealing that local structures responsible for chiral peaking vary with lattice spacing and challenge the Instanton Liquid Model assumptions.

Contribution

It introduces new results with the overlap Dirac operator at various lattice spacings, showing that topological fluctuations are not locally quantized, contrary to previous models.

Findings

Local chirality does not change significantly towards the continuum limit.

Size and density of local structures vary with lattice spacing.

Results disagree with the Instanton Liquid Model assumptions.

Abstract

We discuss the utility of low-lying Dirac eigenmodes for studying the nature of topological charge fluctuations in QCD. The implications of previous results using the local chirality histogram method are discussed, and the new results using the overlap Dirac operator in Wilson gauge backgrounds at lattice spacings ranging from a~0.04 fm to a~0.12 fm are reported. While the degree of local chirality does not change appreciably closer to the continuum limit, we find that the size and density of local structures responsible for chiral peaking do change significantly. The resulting values are in disagreement with the assumptions of the Instanton Liquid Model. We conclude that the fluctuations of topological charge in the QCD vacuum are not locally quantized.