Topology, Random Matrix Theory and the spectrum of the Wilson Dirac operator

Abstract

We study the spectrum of the hermitian Wilson Dirac operator in the epsilon-regime of QCD in the quenched approximation and compare it to predictions from Wilson Random Matrix Theory. Using the distributions of single eigenvalues in the microscopic limit and for specific topological charge sectors, we examine the possibility of extracting estimates of the low energy constants which parametrise the lattice artefacts in Wilson chiral perturbation theory. The topological charge of the field configurations is obtained from a field theoretical definition as well as from the flow of eigenvalues of the hermitian Wilson Dirac operator, and we determine the extent to which the two are correlated.

7 pages, 5 figures, proceedings of the XXIX International Symposium on Lattice Field Theory - Lattice 2011, July 10-16, 2011, Squaw Valley, Lake Tahoe, California

References in corpus (11)

• Random matrix theory and spectral sum rules for the Dirac operator in QCD
• Spectral Density of the QCD Dirac Operator near Zero Virtuality
• Lattice QCD in the epsilon-regime and random matrix theory
• Microscopic Spectrum of the Wilson Dirac Operator
• Spectrum of the Wilson Dirac Operator at Finite Lattice Spacings
• Quark condensate in two-flavor QCD
• Eigenvalue Density of the non-Hermitian Wilson Dirac Operator
• The epsilon regime with Wilson fermions
• Finite-Volume Scaling of the Wilson-Dirac Operator Spectrum
• Observations on the Wilson fermions in the epsilon regime
• Spectral properties of the Wilson Dirac operator in the $\epsilon$-regime

Cited by in corpus (2)

• Mixing of orthogonal and skew-orthogonal polynomials and its relation to Wilson RMT
• The Effect of the Low Energy Constants on the Spectral Properties of the Wilson Dirac Operator