Chirality Correlation within Dirac Eigenvectors from Domain Wall Fermions

Abstract

In the dilute instanton gas model of the QCD vacuum, one expects a strong spatial correlation between chirality and the maxima of the Dirac eigenvectors with small eigenvalues. Following Horvath, {\it et al.} we examine this question using lattice gauge theory within the quenched approximation. We extend the work of those authors by using weaker coupling, $β=6.0$, larger lattices, $16^4$, and an improved fermion formulation, domain wall fermions. In contrast with this earlier work, we find a striking correlation between the magnitude of the chirality density, $|ψ^\dagger(x)γ^5ψ(x)|$, and the normal density, $ψ^\dagger(x)ψ(x)$, for the low-lying Dirac eigenvectors.