SUNY-NTG-94/1 The

The spectrum of the QCD Dirac operator and chiral random matrix theory: the threefold way. Abstract We argue that the spectrum of the QCD Dirac operator near zero virtuality can be described by random matrix theory. As in the case of classical random matrix ensembles of Dyson we have three different cases: the chiral orthogonal ensemble (chGOE), the chiral unitary ensemble (chGUE) and the chiral symplectic ensemble (chGSE). They correspond to gauge groups SU(2) in the fundamental representation, SU(N c), N c ≥ 3 in the fundamental representation, and gauge groups for all N c in the adjoint representation, respectively. The joint probability density reproduces Leutwyler-Smilga sum rules.