Related papers: Massive chiral random matrix ensembles at beta = 1…

We review applications of random matrix theory to QCD at nonzero temperature and chemical potential. The chiral phase transition of QCD and QCD-like theories is discussed in terms of eigenvalues of the Dirac operator. We show that for QCD…

We compare the eigenvalue spectra of the Dirac operator from a simulation with two mass degenerate dynamical chirally improved fermions with Random Matrix Theory. Comparisons with distribution of k-th eigenvalues (k=1,2) in fixed…

We summarize the analytical solution of the Chiral Perturbation Theory for the Hermitian Wilson Dirac operator of $N_c=2$ QCD with quarks in the fundamental representation. Results have been obtained for the quenched microscopic spectral…

Mesons constructed from the quark propagators without the lowest-lying eigenmodes of the Dirac operator reveal not only restored SU(2)_L * SU(2)_R chiral and U(1)_A symmetries, but actually a higher symmetry. All possible chiral and U(1)_A…

We use low lying eigenvectors of the overlap-Dirac operator as a probe of the QCD vacuum. If instantons play a significant role one would expect the low lying eigenmodes of the overlap-Dirac operator to consist mainly of the mixed ``would…

Using relations from random matrix theory, we derive exact expressions for all $n$-point spectral correlation functions of Dirac operator eigenvalues in terms of finite-volume partition functions. This is done for both chiral symplectic and…

We simulate Quantum Chromodynamics (QCD) in four Euclidean dimensions with two (degenerate mass) flavors of dynamical quarks. The Dirac operator we use is the so-called chirally improved Dirac operator. We discuss the algorithm used for the…

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 analyze the smallest Dirac eigenvalues by formulating an effective theory for the QCD Dirac spectrum. We find that in a domain where the kinetic term of the effective theory can be ignored, the Dirac eigenvalues are distributed according…

For QCD at non-zero chemical potential $\mu$, the Dirac eigenvalues are scattered in the complex plane. We define a notion of ordering for individual eigenvalues in this case and derive the distributions of individual eigenvalues from…

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…

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 review the application of random matrix theory (RMT) to chiral symmetry in QCD. Starting from the general philosophy of RMT we introduce a chiral random matrix model with the global symmetries of QCD. Exact results are obtained for…

We prove that QCD in the epsilon-regime of chiral Perturbation Theory is equivalent to chiral Random Matrix Theory for zero and both non-zero real and imaginary chemical potential mu. To this aim we prove a theorem that relates integrals…

We study the spectrum of the QCD Dirac operator near zero virtuality for $N_c =2$. According to a universality argument, it can be described by a random matrix theory with the chiral structure of QCD, but with $real$ matrix elements. Using…

The domain model for the QCD vacuum has previously been developed and shown to exhibit confinement of quarks and strong correlation of the local chirality of quark modes and duality of the background domain-like gluon field. Quark…

In a local gauge-invariant theory with massless Dirac fermions a symmetry of the Lorentz-invariant fermion charge is larger than a symmetry of the Lagrangian as a whole. While the Dirac Lagrangian exhibits only a chiral symmetry, the…

We present simulation results for lattice QCD with light pions. For the quark fields we apply chirally symmetric lattice Dirac operators, in particular the overlap hypercube operator, along with the standard overlap operator for comparison.…

We calculate the spectral function of the QCD Dirac operator using the four-dimensional effective operator constructed from the Mobius domain-wall implementation. We utilize the eigenvalue filtering technique combined with the stochastic…

We derive exact analytical expressions for the spectral density of the Dirac operator at fixed \theta-angle in the microscopic domain of one-flavor QCD. These results are obtained by performing the sum over topological sectors using novel…