Related papers: Random Matrix Theory and Chiral Symmetry in QCD
We investigate the eigenvalue spectrum of the staggered Dirac matrix in two color QCD at finite chemical potential. The profiles of complex eigenvalues close to the origin are compared to a complex generalization of the chiral Gaussian…
Random matrix theory (RMT) is a powerful statistical tool to model spectral fluctuations. In addition, RMT provides efficient means to separate different scales in spectra. Recently RMT has found application in quantum chromodynamics (QCD).…
We investigate the eigenvalues and eigenvectors of the staggered Dirac operator in the vicinity of the chiral phase transition of quenched SU(3) lattice gauge theory. We consider both the global features of the spectrum and the local…
We study the eigenvalues of Dirac operators in QCD with two mass degenerate dynamical fermions. The gauge configurations have been obtained with HMC and the so-called Chirally Improved fermionic action. We compare eigenvalues obtained for…
The distribution of the low-lying QCD Dirac spectrum is analyzed by means of partial quenched chiral perturbation theory. We identify an energy scale below which the valence quark mass dependence of the QCD partition function is given by…
A detailed investigation of the low-energy chiral expansion is presented within a model truncation of QCD. The truncation allows for a phenomenological description of the quark-quark interaction in a framework which maintains the global…
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 discuss how the $1/N_c$ expansion and the chiral random matrix theory ($\chi$RMT) can be used in the study of large-$N_c$ gauge theories. We first clarify the parameter region in which each of these two approaches is valid: while the…
In the low energy domain, Chiral Perturbation Theory parametrizes the small chiral symmetry breaking effects, produced by the quark masses $m_u$, $m_d$ and $m_s$, in terms of order parameters of massless QCD. The latter can then, in…
We propose a new method for simulating QCD at finite density. The method is based on a general factorization property of distribution functions of observables, and it is therefore applicable to any system with a complex action. The…
Approximating the sum over all gauge field configurations in the QCD partition function by a liquid of instantons, we calculate the spectrum of the Dirac operator for two and three colors and for 0, 1 and 2 flavors. We find a remarkable…
We investigate the Dirac eigenvalue spectrum ($\rho(\lambda,m_l)$) to study the microscopic origin of axial anomaly in high temperature phase of QCD. We propose novel relations between the derivatives ($\partial^n \rho(\lambda,m_l)/\partial…
In the last century the non-perturbative regularization of chiral fermions was a long-standing problem. We review how this problem was finally overcome by the formulation of a modified but exact form of chiral symmetry on the lattice. This…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…
This review article provides an overview of random matrix theory (RMT) with a focus on its growing impact on the formulation and inference of statistical models and methodologies. Emphasizing applications within high-dimensional statistics,…
We study universal traits which emerge both in real-world complex datasets, as well as in artificially generated ones. Our approach is to analogize data to a physical system and employ tools from statistical physics and Random Matrix Theory…
Since it was first applied to the study of nuclear interactions by Wigner and Dyson, almost 60 years ago, Random Matrix Theory (RMT) has developed into a field of its own within applied mathematics, and is now essential to many parts of…
It has been proposed that partially quenched chiral perturbation theory can be used together with partially quenched lattice QCD to determine the low-energy constants of real QCD. We point out a complication of this approach and show how it…
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 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…