Related papers: Microscopic Spectrum of the Wilson Dirac Operator
Lattice regularization is used to perform chiral perturbation theory calculations in finite volume. The lattice spacing is chosen small enough to be irrelevant, and numerical results are obtained from simple summations.
The spectrum of the Dirac operator near zero virtuality obtained in lattice gauge simulations is known to be universally described by chiral random matrix theory. We address the question of the maximum energy for which this universality…
We compute the scattering amplitude in Wilson Chiral Perturbation Theory for two flavors. The lattice spacing effects due to the explicit chiral symmetry breaking are kept through O(a^2), and we consider the regime where the quark mass m is…
We have computed ensembles of complete spectra of the staggered Dirac operator using four-dimensional SU(2) gauge fields, both in the quenched approximation and with dynamical fermions. To identify universal features in the Dirac spectrum,…
Effects of dynamical quarks on the microscopic spectrum of the Wilson Dirac operator are analyzed by means of effective field theory. We consider the distributions of the real modes of the Wilson Dirac operator as well as the spectrum of…
It has been shown recently that Dirac operators satisfying the Ginsparg-Wilson relation provide a solution of the chirality problem in QCD at finite lattice spacing. We discuss different ways to construct these operators and their…
We solve a new chiral Random Two-Matrix Theory by means of biorthogonal polynomials for any matrix size $N$. By deriving the relevant kernels we find explicit formulas for all $(n,k)$-point spectral (mixed or unmixed) correlation functions.…
When chiral symmetry is spontaneously broken, the low-energy part of the Dirac operator spectrum can be computed analytically in the chiral limit. The tool is effective field theory or, equivalently in this case, Random Matrix Theory.
We investigate the universal features of chiral symmetry breaking in large-$N$ QCD by comparing non-perturbative determinations of the low-lying Dirac spectrum with chiral Random Matrix Theory (RMT) predictions. Our numerical Monte Carlo…
The importance of the spectral density of the Dirac operator in studying spontaneous chiral symmetry breaking and anomalous U(1) axial symmetry breaking are reviewed. It is shown that both types of symmetry breaking can be traced to effects…
We find the lattice spacing dependence of the eigenvalue density of the non-Hermitian Wilson Dirac operator in the $\epsilon$-domain. The starting point is the joint probability density of the corresponding random matrix theory. In addition…
In this lecture we review recent lattice QCD studies of the statistical properties of the eigenvalues of the QCD Dirac operator. We find that the fluctuations of the smallest Dirac eigenvalues are described by chiral Random Matrix Theories…
We show how the leading physical and Wilson low-energy constants associated with Wilson fermions in lattice gauge theory can be determined individually by using spectral information of the Wilson Dirac operator with fixed index at finite…
In these lectures we review recent results on universal fluctuations of QCD Dirac spectra and applications of Random Matrix Theory (RMT) to QCD. We review general properties of Dirac spectra and discuss the relation between chiral symmetry…
In QCD chiral symmetry is explicitly broken by quark masses, the effect of which can be described reliably by chiral perturbation theory. Effects of explicit chiral symmetry breaking by the lattice regularisation of the Dirac operator,…
We apply chiral perturbation theory to the pseudoscalar meson mass and decay constant data obtained in the PACS-CS Project toward 2+1 flavor lattice QCD simulations with the O(a)-improved Wilson quarks. We examine the existence of chiral…
In these two lectures given at the 1997 Zakopane workshop on "New Developments in Quantum Field Theory" we review recent results on universal fluctuations in QCD Dirac spectra. We start the first lecture with a review of some general…
We compute the microscopic spectrum of the QCD Dirac operator in the presence of dynamical fermions in the framework of random-matrix theory for the chiral Gaussian unitary ensemble. We obtain results for the microscopic spectral…
In the $\varepsilon$-regime of chiral perturbation theory the spectral correlations of the Euclidean QCD Dirac operator close to the origin can be computed using random matrix theory. To incorporate the effect of temperature, a random…
We derive the microscopic spectral density of the Dirac operator in $SU(N_c\geq 3)$ Yang-Mills theory coupled to $N_f$ fermions in the fundamental representation. An essential technical ingredient is an exact rewriting of this density in…