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.

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