Dirac Operator Spectra from Finite-Volume Partition Functions

TL;DR

This paper derives exact formulas for the microscopic spectral correlators of the Dirac operator in certain gauge theories using finite-volume partition functions and their connection to random matrix theory.

Contribution

It provides explicit expressions for spectral correlators of the Dirac operator in $SU(N_c)$ gauge theories with multiple fermions, linking finite-volume partition functions to random matrix theory.

Findings

Exact spectral correlators derived for $SU(N_c)$ gauge theories

Connection established between finite-volume partition functions and random matrix theory

Results applicable to theories with $N_f$ fundamental fermions

Abstract

Based on the relation to random matrix theory, exact expressions for all microscopic spectral correlators of the Dirac operator can be computed from finite-volume partition functions. This is illustrated for the case of $SU(N_c)$ gauge theories with $N_c\geq 3$ and $N_f$ fermions in the fundamental representation.