Quark spectra, topology, and random matrix theory

Quark spectra in QCD are linked to fundamental properties of the theory inc luding the identification of pions as the Goldstone bosons of spontaneously broken chiral symmetry. The lattice overlap Dirac operator provides a nonp erturbative, ultraviolet-regularized description of quarks with the correct chiral symmetry. Properties of the spectrum of this operator and their rel ation to random matrix theory are studied here. In particular, the predicti ons from chiral random matrix theory in topologically nontrivial gauge fiel d sectors are tested for the first time. [S0031-9007(99)09176-0].