Microscopic Spectrum of the Wilson Dirac Operator

TL;DR

This paper develops a theoretical framework combining chiral perturbation theory and random matrix theory to analyze the spectral density of the Wilson Dirac operator, providing new insights into lattice gauge theory at finite lattice spacing.

Contribution

It introduces a novel analytical approach and a chiral Random Matrix Theory model to study the spectral density of the Wilson Dirac operator.

Findings

Derived analytical expressions for spectral density at the scale of average level spacing.

Established a universal scaling function for volume and lattice spacing corrections.

Reproduced spectral density results using a new chiral Random Matrix Theory.

Abstract

We calculate the leading contribution to the spectral density of the Wilson Dirac operator using chiral perturbation theory where volume and lattice spacing corrections are given by universal scaling functions. We find analytical expressions for the spectral density on the scale of the average level spacing, and introduce a chiral Random Matrix Theory that reproduces these results. Our work opens up a novel approach to the infinite volume limit of lattice gauge theory at finite lattice spacing and new ways to extract coefficients of Wilson chiral perturbation theory.