Spectrum of the Wilson Dirac Operator at Finite Lattice Spacings
Abstract
We consider the effect of discretization errors on the microscopic spectrum of the Wilson Dirac operator using both chiral Perturbation Theory and chiral Random Matrix Theory. A graded chiral Lagrangian is used to evaluate the microscopic spectral density of the Hermitian Wilson Dirac operator as well as the distribution of the chirality over the real eigenvalues of the Wilson Dirac operator. It is shown that a chiral Random Matrix Theory for the Wilson Dirac operator reproduces the leading zero-momentum terms of Wilson chiral Perturbation Theory. All results are obtained for fixed index of the Wilson Dirac operator. The low-energy constants of Wilson chiral Perturbation theory are shown to be constrained by the Hermiticity properties of the Wilson Dirac operator.
Keywords
Cite
@article{arxiv.1012.0752,
title = {Spectrum of the Wilson Dirac Operator at Finite Lattice Spacings},
author = {G. Akemann and P. H. Damgaard and K. Splittorff and J. J. M. Verbaarschot},
journal= {arXiv preprint arXiv:1012.0752},
year = {2015}
}
Comments
48 pages, 8 figures,v2 minor corrections same version as published in PRD