QCD with Chemical Potential and Matrix Models

Abstract

In the first section the dynamics of QCD at finite temperature and density are summarized. Color superconductivity that takes place at sufficiently high density and low temperature is reviewed and unsolved problems on the QCD phase diagram are presented. In the second section readers are introduced to QCD with the gauge group SU(2) (called two-color QCD), and the similarities to and differences between this theory and the standard three-color QCD are illustrated. An overview of chiral perturbation theory (ChPT) for two-color QCD is presented and used to discuss the phase diagram at finite density. In the third section the connection between small eigenvalues of the Dirac operator and spontaneous chiral symmetry breaking is delineated by reviewing the Banks-Casher relation, the Smilga-Stern relation and the Leutwyler-Smilga spectral sum rules. Chiral random matrix theory (ChRMT) is then introduced, and the universal correspondence of ChRMT to the e-regime of partially quenched ChPT is explained. Finally existing approaches to applying ChRMT to QCD with nonzero chemical potential are assessed.