Spectral properties of the Wilson Dirac operator in the $\epsilon$-regime

Abstract

We investigate the spectral properties of the Wilson Dirac operator in quenched QCD in the microscopic regime. We distinguish the topological sectors using the index as determined by the Wilson flow method. Consequently, the distributions of the low-lying eigenvalues of the Wilson Dirac operator can be compared in each of the topological sectors to predictions from random matrix theory applied to the $\epsilon$-regime of chiral perturbation theory. We find rather good agreement for volumes as small as $(1.5\text{fm}{)}^4$ and lattice spacings as coarse as $0.1\text{fm}$, and demonstrate that it is indeed possible to extract low-energy constants for Wilson fermions from the spectral properties of the Wilson Dirac operator.

Changed normalizations for some of the results, cosmetic updates to several plots. Conclusions not affected. Version accepted for publication by JHEP. 22 pages, 12 figures

References in corpus (4)

• Eigenvalue Density of the non-Hermitian Wilson Dirac Operator
• The epsilon regime with Wilson fermions
• Finite-Volume Scaling of the Wilson-Dirac Operator Spectrum
• Observations on the Wilson fermions in the epsilon regime

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• Random Matrix Theory and Quantum Chromodynamics
• Individual Eigenvalue Distributions for the Wilson Dirac Operator
• Chiral Dynamics With Wilson Fermions
• Progress on the Microscopic Spectrum of the Dirac Operator for QCD with Wilson Fermions
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