Related papers: Characterization of Universal Behavior in QCD Dira…
We compute the chiral condensate in 2+1-flavor QCD through the spectrum of low-lying eigenmodes of Dirac operator. The number of eigenvalues of the Dirac operator is evaluated using a stochastic method with an eigenvalue filtering technique…
A model for the QCD vacuum based on a domainlike structured background gluon field with definite duality attributed to the domains has been shown elsewhere to give confinement of static quarks, a reasonable value for the topological…
We reveal that the universal scaling properties of the chiral phase transition in quantum chromodynamics (QCD) at the macroscale are, in fact, encoded within the microscopic energy levels of its fundamental constituents, the quarks. We…
We study the spectrum of the QCD Dirac operator for two colors with fermions in the fundamental representation and for two or more colors with adjoint fermions. For $N_f$ flavors, the chiral flavor symmetry of these theories is…
Based on the exact relationship to Random Matrix Theory, we derive the probability distribution of the k-th smallest Dirac operator eigenvalue in the microscopic finite-volume scaling regime of QCD and related gauge theories.
We calculate the chiral condensate of QCD with 2, 2+1 and 3 flavors of sea quarks. Lattice QCD simulations are performed employing dynamical overlap fermions with up and down quark masses covering a range between 3 and 100 MeV. On L ~…
We use a random matrix model to study chiral symmetry breaking in QCD at finite chemical potential $\mu$. We solve the model and compute the eigenvalue density of the Dirac matrix on a complex plane. A naive ``replica trick'' fails for…
These notes are based on the lectures delivered at the Les Houches Summer School in July 2015. They are addressed at a mixed audience of physicists and mathematicians with some basic working knowledge of random matrix theory. The first part…
We formulate a random matrix model which mimics the chiral phase transition in QCD with two light flavors. Two critical exponents are calculated. We obtain the mean field values $\beta = \frac 12 $ and $\delta = 3$. We also find that the…
Quark spectra in QCD are linked to fundamental properties of the theory including the identification of pions as the Goldstone bosons of spontaneously broken chiral symmetry. The lattice Overlap-Dirac operator provides a nonperturbative,…
The use of the absolute measure of local chirality is championed since it has a uniform distribution for randomly reshuffled chiral components so that any deviations from uniformity in the associated "X-distribution" are directly…
The properties of the spectrum of the overlap Dirac operator and their relation to random matrix theory are studied. In particular, the predictions from chiral random matrix theory in topologically non-trivial gauge field sectors are…
Recent work on the spectrum of the Euclidean Dirac operator spectrum show that the exact microscopic spectral density can be computed in both random matrix theory, and directly from field theory. Exact relations to effective Lagrangians…
We compare analytic predictions of non-Hermitian chiral random matrix theory with the complex Dirac operator eigenvalue spectrum of two-colour lattice gauge theory with dynamical fermions at nonzero chemical potential. The Dirac eigenvalues…
We demonstrate the universality of the spectral correlation functions of a QCD inspired random matrix model that consists of a random part having the chiral structure of the QCD Dirac operator and a deterministic part which describes a…
The spectral density of euclidean Dirac operator is investigated in partially quenched QCD with arbitrary quark masses. A representation of scalar and pseudoscalar correlators in terms of the spectral density is discussed. The spectral…
We analyze the eigenvalue statistics of the staggered Dirac operator above $T_{c}$ in QCD with 2+1 flavors of dynamical quarks. We use physical quark masses in our simulations. We compare the eigenvalue statistics from several parts of the…
Some exact relations for the spectral density $\rho(\lambda)$ of the Euclidean Dirac operator in $QCD$ are derived. They follow directly from the chiral symmetry of the $QCD$ lagrangian with massless quarks. New results are obtained both in…
We calculate the spectral density of the Dirac operator over an ensemble of configurations composed of overlapping instantons and anti-instantons. We find evidence that the spectral density diverges in the limit of small eigenvalues. This…
We derive an analytical expression for the distribution of the k-th smallest Dirac eigenvalue in QCD with imaginary isospin chemical potential in the Dirac operator. Because of its dependence on the pion decay constant F through the…