Chirality Correlation within Dirac Eigenvectors from Domain Wall Fermions

TL;DR

This paper investigates the spatial correlation between chirality and Dirac eigenvector maxima in lattice QCD, revealing a strong link using improved methods and larger lattices, supporting instanton-based models.

Contribution

It extends previous lattice studies by employing weaker coupling, larger lattices, and domain wall fermions, demonstrating a pronounced chirality correlation in Dirac eigenvectors.

Findings

Strong correlation between chirality density and eigenvector magnitude

Supports instanton gas model predictions

Uses improved lattice techniques and larger volumes

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, $\beta=6.0$, 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 magnitude of the chirality density, $|\psi^\dagger(x)\gamma^5\psi(x)|$, and the normal density, $\psi^\dagger(x)\psi(x)$, for the low-lying Dirac eigenvectors.