Related papers: Topology and chiral random matrix theory at nonzer…
Recently, QCD Dirac spectra have been obtained for reasonably large lattices. We argue that correlations of these spectra are universal and can be obtained from a random matrix model with the global symmetries of QCD. Analytical arguments…
In this talk we present the results published recently in Ref. [1], where we showed how to introduce a quark chemical potential in the overlap Dirac operator. The resulting operator satisfies a Ginsparg-Wilson relation and has exact zero…
The topological susceptibility and the higher moments of the topological charge distribution in QCD are expressed through certain n-point functions of the scalar and pseudo-scalar quark densities at vanishing momenta, which are free of…
We discuss random matrix models for the spontaneous breaking of both chiral and color symmetries at zero chemical potential and finite temperature. Exploring different Lorentz and gauge symmetric color structures of the random matrix…
Eigenvalues and eigenfunctions of the QCD Dirac operator are studied for an instanton liquid partition function. We find that for energy differences $\delta E$ below an energy scale $E_c$, identified as the Thouless energy, the eigenvalue…
At low temperature the low-lying QCD Dirac spectrum obeys random matrix statistics. Recently we found that above $T_{c}$ the lowest part of the spectrum consists of localized modes that obey Poisson statistics. An interesting implication of…
Within the framework of SU(2) chiral perturbation theory, we derive the general solution of the QCD $\theta$-vacuum for an arbitrary vacuum phase, explicitly incorporating isospin-breaking effects from the light quark mass difference, and…
Recently, a non-Hermitian chiral random matrix model was proposed to describe the eigenvalues of the QCD Dirac operator at nonzero chemical potential. This matrix model can be constructed from QCD by mapping it to an equivalent matrix model…
Random Matrix Theory has been a unifying approach in physics and mathematics.In these lectures we discuss applications of Random Matrix Theory to QCD and emphasize underlying integrable structures. In the first lecture we give an overview…
In this chapter of the Oxford Handbook of Random Matrix Theory we introduce chiral Random Matrix Theories with the global symmetries of QCD. In the microscopic domain, these theories reproduce the mass and chemical potential dependence of…
In the $\epsilon$-domain of QCD we have obtained exact analytical expressions for the eigenvalue density of the Dirac operator at fixed $\theta \ne 0$ for both one and two flavors. These results made it possible to explain how the different…
We model the effects of a large number of zero and near-zero modes in the QCD partition function by using sparse chiral matrix models with an emphasis on the quenched topological susceptibility in the choice of the measure. At finite…
We discuss the utility of low-lying Dirac eigenmodes for studying the nature of topological charge fluctuations in QCD. The implications of previous results using the local chirality histogram method are discussed, and the new results using…
We discuss properties of thermal Quantum Chromodynamics obtained by means of lattice simulations with overlap fermions. This fermion discretisation preserves chiral symmetry at finite lattice spacing. We present details of the formulation…
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…
In this lecture we argue that the fluctuations of Dirac eigenvalues on the finest scale, i.e. on the scale of the average level spacing do not depend on the underlying dynamics and can be obtained from a chiral random matrix theory with the…
The correlations of the QCD Dirac eigenvalues are studied with use of an extended chiral random matrix model. The inclusion of spatial dependence which the original model lacks enables us to investigate the effects of diffusion modes. We…
The low energy eigenmodes of the continuum QCD Dirac operator are extended, but on the lattice, due to discretization effects, the Dirac operator can have localized eigenmodes. These non-physical modes can introduce strong lattice artifacts…
Using an integration formula recently derived by Conrey, Farmer and Zirnbauer, we calculate the expectation value of the phase factor of the fermion determinant for the staggered lattice QCD action in one dimension. We show that the…
We investigate and clarify the role of topology and the issues surrounding the epsilon regime for staggered quarks. We study unimproved and improved staggered quark Dirac operators on quenched lattice QCD gluon backgrounds generated using a…