Related papers: Characterization of Universal Behavior in QCD Dira…
For quantifying the universal properties of the chiral phase transition in QCD through numerical calculations on a discrete space-time lattice, one needs to perform controlled extrapolations to the continuum and infinite-volume limits…
We show that the spectrum of the Dirac operator in complex Langevin simulations of QCD at non-zero chemical potential must behave in a way which is radically different from the one in simulations with ordinary non-complexified gauge fields:…
We compute by Monte Carlo methods the individual distributions of the $k$th smallest Dirac operator eigenvalues in QCD, and compare them with recent analytical predictions. We do this for both massless and massive quarks in an SU(3) gauge…
By matching 1/m^2 divergences in finite-volume two-point correlation functions of the scalar or pseudoscalar densities with those obtained in chiral perturbation theory, we derive a relation between the Dirac operator zero-mode…
It was established that distribution of the near-zero modes of the Dirac operator is consistent with the Chiral Random Matrix Theory (CRMT) and can be considered as a consequence of spontaneous breaking of chiral symmetry (SBCS) in QCD. The…
We calculate numerically the eigenvalue distribution of the overlap Dirac operator in the quenched Schwinger model on a lattice. The distribution does not fit any of the three universality classes of spontaneous chiral symmetry breaking,…
We provide first evidence that Matrix Models describe the low lying complex Dirac eigenvalues in a theory with dynamical fermions at non-zero density. Lattice data for gauge group SU(2) with staggered fermions are compared to detailed…
We compute statistical distributions of individual low-lying eigenvalues of random matrix ensembles interpolating chiral Gaussian symplectic and unitary ensembles. To this aim we use the Nystrom-type discretization of Fredholm Pfaffians and…
Using the Gell-Mann-Oakes-Renner (GOR) relation and semi-classical arguments, we show that the bulk quark spectrum in QCD exhibits a variety of regimes including the ergodic one described by random matrix theory. We analyze the quark…
We analyze the eigenvalue spectrum of the staggered Dirac matrix in two-color QCD at nonzero baryon density when the eigenvalues become complex. The quasi-zero modes and their role for chiral symmetry breaking and the deconfinement…
We derive a hydrodynamical description of the eigenvalues of the chiral Dirac spectrum in the vacuum and in the large $N$ (volume) limit. The linearized hydrodynamics supports sound waves. The stochastic relaxation of the eigenvalues is…
We suggest that the spectral properties near zero virtuality of three dimensional QCD, follow from a Hermitean random matrix model. The exact spectral density is derived for this family of random matrix models both for even and odd number…
We propose a new way of understanding how chiral symmetry is realized in the high temperature phase of QCD. Based on the finding that a simple free instanton gas precisely describes the details of the lowest part of the spectrum of the…
We examine quenched chiral logarithms in lattice QCD with overlap Dirac quarks. From our data of m_pi^2, we determine the coefficient of quenched chiral logarithm delta = 0.203(14), 0.176(17), 0.193(17) and 0.200(13) for lattices of sizes…
The aim of this introductory lecture is to review the arguments, according to which the symmetry properties of the strong interaction reveal themselves at low energies. I first discuss the symmetries of QCD, then sketch the method used to…
The zero momentum sectors in effective theories of three dimensional QCD coupled to pseudoreal (two colors) and real (adjoint) quarks in a classically parity-invariant manner have alternative descriptions in terms of orthogonal and…
We present two pieces of evidence in support of the conjecture that the microscopic spectral density of the Dirac operator is a universal quantity. First, we compare lattice data to predictions from random matrix theory. Second, we show…
Chiral dynamics makes definitive predictions for the electromagnetic polarizabilities of hadrons near the chiral limit; but, agreement with experiment is tenuous in some cases. We provide an overview of lattice QCD methods to compute the…
We revisit the concept of chiral disorder in QCD in the presence of a QED magnetic field |eH|. Weak magnetism corresponds to |eH| < 1/rho^2 with rho\approx (1/3) fm the vacuum instanton size, while strong magnetism the reverse. Asymptotics…
Using the graded eigenvalue method and a recently computed extension of the Itzykson-Zuber integral to complex matrices, we compute the $k$-point spectral correlation functions of the Dirac operator in a chiral random matrix model with a…