Microscopic Spectra of Dirac Operators and Finite-Volume Partition Functions

TL;DR

This paper uses random matrix theory to analyze the connection between microscopic Dirac spectra and finite-volume partition functions across different universality classes of gauge theories, providing new insights into universality.

Contribution

It systematically relates microscopic Dirac spectra to finite-volume partition functions for various matrix ensembles, expanding the understanding of universality in gauge theories.

Findings

Established exact relationships for unitary ensemble

Extended analysis to orthogonal and symplectic ensembles

Reconsidered the concept of universality in this context

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 $SU(N_c)$ gauge theories with $N_f$ fermions in different representations. Random matrix theory universality is reconsidered in this new light.