Low-Lying Dirac Eigenmodes, Topological Charge Fluctuations and the Instanton Liquid Model

TL;DR

This study investigates the structure of low-lying Dirac eigenmodes in QCD and finds they do not align with the instanton liquid model's assumptions, challenging its validity for explaining chiral symmetry breaking.

Contribution

The paper provides evidence that low-lying Dirac eigenmodes cannot be described by instanton-based zeromodes, questioning the instanton liquid model's applicability in QCD.

Findings

Low-lying eigenmodes are not linear combinations of 't Hooft zeromodes.

Instanton liquid scenario for chiral symmetry breaking is not supported.

Topological charge fluctuations are not dominated by localized unit charge lumps.

Abstract

The local structure of low-lying eigenmodes of the overlap Dirac operator is studied. It is found that these modes cannot be described as linear combinations of 't Hooft "would-be" zeromodes associated with instanton excitations that underly the Instanton Liquid Model. This implies that the instanton liquid scenario for spontaneous chiral symmetry breaking in QCD is not accurate. More generally, our data suggests that the vacuum fluctuations of topological charge are not effectively dominated by localized lumps of unit charge with which the topological "would-be" zeromodes could be associated.