Spectrum of the Wilson Dirac Operator at Finite Lattice Spacings

Details Spectrum of the Wilson Dirac Operator at Finite Lattice Spacings Spectrum of the Wilson Dirac Operator at Finite Lattice Spacings

2010-12-03

arxiv.org/abs/1012.0752v2

Phys.Rev.D83:085014,2011

Physics

High Energy Physics

High Energy Physics - Lattice

48 pages, 8 figures,v2 minor corrections same version as published in PRD

Scientific paper

10.1103/PhysRevD.83.085014

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.

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