Random Matrices and Chiral Symmetry in QCD

Abstract

In this talk we review some recent results from random matrix models as applied to some non-perturbative issues in QCD. All of the issues we will discuss touched upon the important phenomenon related to the spontaneous breaking of chiral symmetry. The afore mentioned insights are: 1. Spontaneous breakdown of chiral symmetry and disorder. 2. Universal microscopic properties of the eigenvalues of the Dirac operator in the vacuum. 3. Universal microscopic properties of the eigenvalues of the Dirac operator in matter. 4. Structural changes of the Dirac spectrum - finite temperature. 5. Structural changes of the Dirac spectrum - finite baryonic density - ``phony vacua'' 6. Structural changes of the Dirac spectrum - finite baryonic density - ``true vacua'' . 7. Phase diagram. 8. Critical parameters. 9. Critical exponents. 10. $U(1)_A$ problem. 11. Screening of the pseudoscalar susceptibility. 12. Strong CP violation (finite $\theta$).