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

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.