Microscopic Spectra of Dirac Operators and Finite-Volume Partition Functions

Akemann G, Damgaard PH. Microscopic Spectra of Dirac Operators and Finite-Volume Partition Functions. Nucl.Phys. B. 1998;528(1-2):411-431.Exact results from random matrix theory are used to systematically analysethe relationship between microscopic Dirac spectra and finite-volume partitionfunctions. Results are presented for the unitary ensemble, and the chiralanalogs of the three classical matrix ensembles: unitary, orthogonal andsymplectic, all of which describe universality classes of $SU(N_c)$ gaugetheories with $N_f$ fermions in different representations. Random matrix theoryuniversality is reconsidered in this new light