Spectrum of the Wilson Dirac Operator at Finite Lattice Spacings

Akemann G, Damgaard PH, Splittorff K, Verbaarschot JJM. Spectrum of the Wilson Dirac Operator at Finite Lattice Spacings. Phys. Rev. D. 2011;83(8): 85014.We consider the effect of discretization errors on the microscopic spectrumof the Wilson Dirac operator using both chiral Perturbation Theory and chiralRandom Matrix Theory. A graded chiral Lagrangian is used to evaluate themicroscopic spectral density of the Hermitian Wilson Dirac operator as well asthe distribution of the chirality over the real eigenvalues of the Wilson Diracoperator. It is shown that a chiral Random Matrix Theory for the Wilson Diracoperator reproduces the leading zero-momentum terms of Wilson chiralPerturbation Theory. All results are obtained for fixed index of the WilsonDirac operator. The low-energy constants of Wilson chiral Perturbation theoryare shown to be constrained by the Hermiticity properties of the Wilson Diracoperator