Handbook Article on Applications of Random Matrix Theory to QCD

Abstract

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.

31 pages, 5 figures. Invited article for the Oxford Handbook of Random Matrix Theory

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• Universal shocks in random matrix theory
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Cited by in corpus (9)

• Random Matrix Theory for the Hermitian Wilson Dirac Operator and the chGUE-GUE Transition
• Moments of Wishart-Laguerre and Jacobi ensembles of random matrices: application to the quantum transport problem in chaotic cavities
• Random matrix theory of unquenched two-colour QCD with nonzero chemical potential
• The Riemann zeros as energy levels of a Dirac fermion in a potential built from the prime numbers in Rindler spacetime
• New universality classes of the non-Hermitian Dirac operator in QCD-like theories
• Non-Hermitian extensions of Wishart random matrix ensembles
• GUE-chGUE Transition preserving Chirality at finite Matrix Size
• Universality Conjecture for all Airy, Sine and Bessel Kernels in the Complex Plane
• Dissipation and decoherence for generic open quantum systems