Microscopic spectra of Dirac operators and finite-volume partition functions

Exact results from random matrix theory are used to systematically analyze the relationship between microscopic Dirac spectra and finite-volume partition functions. Results are presented for the unitary ensemble, and the chiral analogs of the three classical matrix ensembles: unitary, orthogonal and symplectic, all of which describe universality classes of SU(N-c) gauge theories with N-f fermions in different representations. Random matrix theory universality is reconsidered in this new light. (C) 1998 Elsevier Science B.V.