Microscopic spectra of dirac operators and finite-volume partition functions

Abstract

Exact results from random matrix theory are used to systematically analyse 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(Nc) gauge theories with Nf fermions in different representations. Random matrix theory universality is reconsidered in this new light.