Chiral Random Matrix Models in QCD

Abstract

We review some motivation behind the introduction of chiral random matrix models in QCD, with particular emphasis on the importance of the Gell-Mann-Oakes (GOR) relation for these arguments. We show why the microscopic limit is universal in power counting, and present arguments for why the macroscopic limit is generic for a class of problems that defy power counting, examples being the strong CP and U(1) problems. Some new results are discussed in light of recent lattice simulations.

Comments: 32 pages with 13 EPS figures included. Paper based on talks given by the Authors at Kyoto, Bielefeld, Trento and Zakopane