Random matrix theory and chiral symmetry in QCD

JJM Verbaarschot, T Wettig - Annual Review of Nuclear and …, 2000 - annualreviews.org
▪ Abstract Random matrix theory is a powerful way to describe universal correlations of
eigenvalues of complex systems. It also may serve as a schematic model for disorder in …

Recent exact and asymptotic results for products of independent random matrices

G Akemann, JR Ipsen - arxiv preprint arxiv:1502.01667, 2015 - arxiv.org
In this review we summarise recent results for the complex eigenvalues and singular values
of finite products of finite size random matrices, their correlation functions and asymptotic …

Symmetry classification of many-body Lindbladians: Tenfold way and beyond

L Sá, P Ribeiro, T Prosen - Physical Review X, 2023 - APS
We perform a systematic symmetry classification of many-body Lindblad superoperators
describing general (interacting) open quantum systems coupled to a Markovian …

Phase diagram of QCD

MA Halasz, AD Jackson, RE Shrock, MA Stephanov… - Physical Review D, 1998 - APS
We analyze the phase diagram of QCD with two massless quark flavors in the space of
temperature T and chemical potential of the baryon charge μ using available experimental …

Functional integrals for QCD at nonzero chemical potential and zero density

TD Cohen - Physical review letters, 2003 - APS
In a Euclidean space functional integral treatment of the free energy of QCD, a chemical
potential enters only through the functional determinant of the Dirac operator which for any …

Renormalization and running of quark mass and field in the regularization invariant and MS schemes at three and four loops

KG Chetyrkin, A Retey - Nuclear Physics B, 2000 - Elsevier
We derive explicit transformation formulae relating the renormalized quark mass and field as
defined in the MS-scheme with the corresponding quantities defined in any other scheme …

Nonperturbative investigations of SU (3) gauge theory with eight dynamical flavors

T Appelquist, RC Brower, GT Fleming, A Gasbarro… - Physical Review D, 2019 - APS
We present our lattice studies of SU (3) gauge theory with N f= 8 degenerate fermions in the
fundamental representation. Using nHYP-smeared staggered fermions we study finite …

From chiral random matrix theory to chiral perturbation theory

JC Osborn, D Toublan, JJM Verbaarschot - Nuclear Physics B, 1999 - Elsevier
We study the spectrum of the QCD Dirac operator by means of the valence quark mass
dependence of the chiral condensate in partially quenched Chiral Perturbation Theory …

The microscopic spectral density of the QCD Dirac operator

PH Damgaard, JC Osborn, D Toublan… - Nuclear Physics B, 1999 - Elsevier
We derive the microscopic spectral density of the Dirac operator in SU (Nc⩾ 3) Yang-Mills
theory coupled to Nf fermions in the fundamental representation. An essential technical …

Generation of matrix models by Ŵ-operators

A Morozov, S Shakirov - Journal of High Energy Physics, 2009 - iopscience.iop.org
We show that partition functions of various matrix models can be obtained by acting on
elementary functions with exponents of Ŵ operators. A number of illustrations is given …