Local chirality of low-lying Dirac eigenmodes and the instanton liquid model

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 instantonlike fluctuations. The results with the overlap Dirac operator in Wilson gauge backgrounds at lattice spacings ranging from a≈0.04fm to a≈0.12fm 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.