Related papers: Random matrix theory and spectral sum rules for th…
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 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…
We consider random matrix models for the thermodynamic competition between chiral symmetry breaking and diquark condensation in QCD at finite temperature and finite baryon density. The models produce mean field phase diagrams whose topology…
We investigate the universal features of chiral symmetry breaking in large-$N$ QCD by comparing non-perturbative determinations of the low-lying Dirac spectrum with chiral Random Matrix Theory (RMT) predictions. Our numerical Monte Carlo…
Recently Magnea hep-th/9907096 , hep-th/9912207 [Phys.Rev.D61, 056005 (2000); Phys.Rev.D62, 016005 (2000)] claimed to have computed the first sum rules for Dirac operators in 3D gauge theories from 0D non-linear sigma models. I point out…
Exact results from random matrix theory are used to systematically analyse the relationship between microscopic Dirac spectra and finite-volume partition functions. Results are presented for the unitary ensemble, and the chiral analogs of…
Universality in unitary invariant random matrix ensembles with complex matrix elements is considered. We treat two general ensembles which have a determinant factor in the weight. These ensembles are relevant, e.g., for spectra of the Dirac…
In traditional QCD sum rules, the simple hadron spectral density model of ``delta-function-type ground state + theta-function-type continuous spectrum" determines that there is no perfect parameter selection. In recent years, inverse…
In the epsilon-regime of QCD the main features of the spectrum of the low-lying eigenvalues of the (euclidean) Dirac operator are expected to be described by a certain universality class of random matrix models. In particular, the latter…
Recently, Son and Stephanov have considered an "open moose" as a possible dual model of a QCD-like theory of chiral symmetry breaking. In this note we demonstrate that although the Weinberg sum rules are satisfied in any such model, the…
Let $\a$ be a complex random variable with mean zero and bounded variance $\sigma^{2}$. Let $N_{n}$ be a random matrix of order $n$ with entries being i.i.d. copies of $\a$. Let $\lambda_{1}, ..., \lambda_{n}$ be the eigenvalues of…
We investigate the universality of microscopic eigenvalue correlations for Random Matrix Theories with the global symmetries of the QCD partition function. In this article we analyze the case of real valued chiral Random Matrix Theories…
We consider sum rules of the Weinberg type at zero and nonzero temperatures. On the basis of the operator product expansion at zero temperature we obtain a new sum rule which involves the average of a four-quark operator on one side and…
The near-zero modes of the Dirac operator are connected to spontaneous breaking of chiral symmetry in QCD (SBCS) via the Banks-Casher relation. At the same time the distribution of the near-zero modes is well described by the Random Matrix…
Large ensembles of complete spectra of the Euclidean Dirac operator for staggered fermions are calculated for SU(2) lattice gauge theory. The accumulation of eigenvalues near zero is analyzed as a signal of chiral symmetry breaking and…
Random Matrix Theory (RMT) has elaborated successful predictions for Dirac spectra in field theoretical models. However, a generic assumption by RMT has been a non-vanishing chiral condensate $\Sigma$ in the chiral limit. Here we consider…
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…
We analyze QCD and Weinberg-type sum rules in a low-temperature pion gas using vector and axial-vector spectral functions following from the model-independent chiral-mixing scheme. Toward this end we employ recently constructed vacuum…
We discuss a new Random Matrix Model for QCD with a chemical potential that is based on the symmetries of the Dirac operator and can be solved exactly for all eigenvalue correlations for any number of flavors. In the microscopic limit of…
We link the spontaneous breakdown of chiral symmetry in Euclidean QCD to the collision of spectral shock waves in the vicinity of zero eigenvalue of Dirac operator. The mechanism, originating from complex Burger's-like equation for viscid,…