Microscopic Spectral Density of the Wilson Dirac Operator for One Flavor

TL;DR

This paper analyzes how non-zero lattice spacing affects the spectral density of the Wilson Dirac operator for one flavor, providing analytical results for the chiral condensate and spectral density, and revealing a subtle mechanism for condensate recovery.

Contribution

It offers new analytical insights into the microscopic spectral density and chiral condensate behavior of Wilson fermions at finite lattice spacing for one flavor.

Findings

Analytical expressions for the chiral condensate and spectral density.

Identification of a mechanism ensuring condensate recovery across sectors.

Insights into lattice spacing effects on Wilson fermions.

Abstract

We consider the effect of a non-zero lattice spacing on the low-energy effective theory of Wilson fermions with one flavor. Analytical results are given for both the chiral condensate and the microscopic spectral density of the Wilson Dirac operator. A subtle mechanism ensures that a constant chiral condensate is recovered, once the sum over sectors of fixed index is performed.