Spectrum of the Wilson Dirac operator at finite lattice spacings

TY - JOUR

T1 - Spectrum of the Wilson Dirac operator at finite lattice spacings

AU - Akemann, G.

AU - Damgaard, Poul Henrik

AU - Splittorff, Kim

AU - Verbaarschot, J.J.M.

PY - 2011/4/12

Y1 - 2011/4/12

N2 - 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 a 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.

AB - 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 a 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.

U2 - 10.1103/PhysRevD.83.085014

DO - 10.1103/PhysRevD.83.085014

M3 - Journal article

SN - 2470-0010

VL - 83

SP - 085014

JO - Physical Review D

JF - Physical Review D

IS - 8

ER -