The Low-lying Dirac Eigenmodes from Domain Wall Fermions

TL;DR

This paper computes low-lying eigenmodes of the domain wall Dirac operator to analyze chiral symmetry breaking and topological features in gauge fields, providing insights into the spectral density and residual mass effects.

Contribution

It introduces a method to calculate and analyze low-lying eigenvalues and eigenvectors of the hermitian domain wall Dirac operator, linking spectral properties to physical and topological characteristics.

Findings

Spectral density relates to the chiral condensate via Banks-Casher relation.

Residual chiral symmetry breaking effects are quantified per eigenmode.

Topological structures are probed through matrix elements between eigenmodes.

Abstract

We calculate the low-lying eigenvalues and eigenvectors of the hermitian domain wall Dirac operator on various gauge backgrounds by Ritz minimization. The mass dependence of these eigenvalues is studied to extract the physical 4 dimensional $\lambda$, whose spectral density is related to $<\bar{\psi} \psi>$ through the Banks-Casher relation, and $\delta m$, which represents the effects of the residual chiral symmetry breaking in domain wall formalism on a per eigenmode basis. The topological structure of the underlying gauge field is examined by measuring the $\Gamma_5$ matrix elements between the low-lying eigenmodes.