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Related papers: Random Matrix Theory and Chiral Symmetry in QCD

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We apply a complex chiral random matrix model as an effective model to QCD with a small chemical potential at zero temperature. In our model the correlation functions of complex eigenvalues can be determined analytically in two different…

High Energy Physics - Lattice · Physics 2017-08-23 G. Akemann , T. Wettig

The Random Matrix Model approach to Quantum Chromodynamics (QCD) with non-vanishing chemical potential is reviewed. The general concept using global symmetries is introduced, as well as its relation to field theory, the so-called epsilon…

High Energy Physics - Theory · Physics 2008-11-26 G. Akemann

In these two lectures given at the 1997 Zakopane workshop on "New Developments in Quantum Field Theory" we review recent results on universal fluctuations in QCD Dirac spectra. We start the first lecture with a review of some general…

High Energy Physics - Theory · Physics 2007-05-23 J. J. M. Verbaarschot

Chiral random matrix theory makes very detailed predictions for the spectral correlations of the QCD Dirac operator, both in the bulk of the spectrum and near zero virtuality. These predictions have been successfully tested in lattice QCD…

High Energy Physics - Lattice · Physics 2007-05-23 Tilo Wettig

In a deep-infrared (ergodic) regime, QCD coupled to massive pseudoreal and real quarks are described by chiral orthogonal and symplectic ensembles of random matrices. Using this correspondence, general expressions for the QCD partition…

High Energy Physics - Theory · Physics 2009-10-31 T. Nagao , S. M. Nishigaki

Recently, QCD Dirac spectra have been obtained for reasonably large lattices. We argue that correlations of these spectra are universal and can be obtained from a random matrix model with the global symmetries of QCD. Analytical arguments…

High Energy Physics - Phenomenology · Physics 2009-09-25 J. J. M. Verbaarschot

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…

High Energy Physics - Lattice · Physics 2009-11-10 James C. Osborn

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…

High Energy Physics - Phenomenology · Physics 2008-11-26 K. Splittorff , J. J. M. Verbaarschot

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…

High Energy Physics - Lattice · Physics 2009-11-10 Leonardo Giusti , Martin Lüscher , Peter Weisz , Hartmut Wittig

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…

High Energy Physics - Lattice · Physics 2009-10-28 M. A. Stephanov

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…

High Energy Physics - Theory · Physics 2008-11-26 B. Klein , J. J. M. Verbaarschot

We investigate the eigenvalue spectrum of the staggered Dirac matrix in SU(3) gauge theory and in full QCD as well as in quenched U(1) theory. As a measure of the fluctuation properties of the eigenvalues, we consider the nearest-neighbor…

High Energy Physics - Lattice · Physics 2009-10-31 Elmar Bittner , Harald Markum , Rainer Pullirsch

We establish a relationship between the zeros of the partition function in the complex mass plane and the spectral properties of the Dirac operator in QCD. This relation is derived within the context of chiral Random Matrix Theory and…

High Energy Physics - Theory · Physics 2009-11-07 A. D. Jackson , C. B. Lang , M. Oswald , K. Splittorff

We analyze how individual eigenvalues of the QCD Dirac operator at nonzero quark chemical potential are distributed in the complex plane. Exact and approximate analytical results for both quenched and unquenched distributions are derived…

High Energy Physics - Lattice · Physics 2008-11-26 G. Akemann , J. Bloch , L. Shifrin , T. Wettig

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…

High Energy Physics - Lattice · Physics 2009-01-14 Gernot Akemann , Jacques Bloch , Leonid Shifrin , Tilo Wettig

We investigate the eigenvalue spectrum of the staggered Dirac matrix in full QCD with two colors and finite chemical potential. Along the strong-coupling axis up to the temperature phase transition, the low-lying Dirac spectrum is well…

High Energy Physics - Lattice · Physics 2007-05-23 Elmar Bittner , Maria-Paola Lombardo , Harald Markum , Rainer Pullirsch

We investigate the eigenvalue spectrum of the staggered Dirac matrix in two-color QCD at nonzero temperature and at baryon density when the eigenvalues become complex. The quasi-zero modes and their role for chiral symmetry breaking and the…

High Energy Physics - Phenomenology · Physics 2007-05-23 Elmar Bittner , Maria-Paola Lombardo , Harald Markum , Rainer Pullirsch

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…

High Energy Physics - Lattice · Physics 2015-05-20 Mario Kieburg , Jacobus Verbaarschot , Savvas Zafeiropoulos

As was shown by Leutwyler and Smilga, the fact that chiral symmetry is broken and the existence of a effective finite volume partition function leads to an infinite number of sum rules for the eigenvalues of the Dirac operator in QCD. In…

High Energy Physics - Theory · Physics 2009-09-25 Jacobus Verbaarschot

We summarise recent results for the chiral Random Two-Matrix Theory constructed to describe QCD in the epsilon-regime with imaginary chemical potential. The virtue of this theory is that unquenched Lattice simulations can be used to…

High Energy Physics - Theory · Physics 2008-11-26 G. Akemann