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In this chapter of the Oxford Handbook of Random Matrix Theory we introduce chiral Random Matrix Theories with the global symmetries of QCD. In the microscopic domain, these theories reproduce the mass and chemical potential dependence of QCD. The main focus of this chapter is on the spectral properties of the QCD Dirac operator and relations between chiral Random Matrix Theories and chiral Lagrangians. Both spectra of the anti-hermitian Dirac operator and spectra of the nonhermitian Dirac operator at nonzero chemical potential are discussed.
We compute individual distributions of low-lying eigenvalues of massive chiral random matrix ensembles by the Nystrom-type quadrature method for evaluating the Fredholm determinant and Pfaffian that represent the analytic continuation of the Janossy
We study the correlation functions of Coulomb branch operators of four-dimensional $mathcal{N} = 2$ Superconformal Field Theories (SCFTs). We focus on rank-one theories, such as the SU(2) gauge theory with four fundamental hypermultiplets. Extremal c
We present some applications of central limit theorems on mesoscopic scales for random matrices. When combined with the recent theory of homogenization for Dyson Brownian Motion, this yields the universality of quantities which depend on the behavior
In this article, using the principles of Random Matrix Theory (RMT), we give a measure of quantum chaos by quantifying Spectral From Factor (SFF) appearing from the computation of two-point Out of Time Order Correlation function (OTOC) expressed in t
We propose a random matrix theory for QCD in three dimensions with a Chern-Simons term at level $k$ which spontaneously breaks the flavor symmetry according to U($2N_{rm f}$) $to $ U($N_{rm f}+k$)$times$U($N_{rm f}-k$). This random matrix model is ob