Topology, Random Matrix Theory and the spectrum of the Wilson Dirac operator

TL;DR

This paper investigates the spectrum of the hermitian Wilson Dirac operator in lattice QCD, comparing it with Wilson Random Matrix Theory predictions to extract low energy constants and analyze topological charge correlations.

Contribution

It introduces a method to compare the spectrum with Wilson RMT and assesses topological charge determination techniques in the epsilon-regime of QCD.

Findings

Eigenvalue distributions match Wilson RMT predictions in the microscopic limit.

Topological charge from field theory correlates with eigenvalue flow analysis.

Estimates of low energy constants are obtained from spectral data.

Abstract

We study the spectrum of the hermitian Wilson Dirac operator in the epsilon-regime of QCD in the quenched approximation and compare it to predictions from Wilson Random Matrix Theory. Using the distributions of single eigenvalues in the microscopic limit and for specific topological charge sectors, we examine the possibility of extracting estimates of the low energy constants which parametrise the lattice artefacts in Wilson chiral perturbation theory. The topological charge of the field configurations is obtained from a field theoretical definition as well as from the flow of eigenvalues of the hermitian Wilson Dirac operator, and we determine the extent to which the two are correlated.