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 Horváth 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, $\beta =6.0,$ 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 magnitudes of the chirality density, $|{\psi }^{†}\mathrm{}\left(x\right)\mathrm{}{\gamma }^5\psi \mathrm{}\left(x\right)\mathrm{}|,$ and the normal density, ${\psi }^{†}\mathrm{}\left(x\right)\mathrm{}\psi \mathrm{}\left(x\right),$ for the low-lying Dirac eigenvectors.

• Received 11 May 2001

DOI:https://doi.org/10.1103/PhysRevD.65.014504