Distributions of Dirac Operator Eigenvalues

TL;DR

This paper derives the distribution of individual Dirac eigenvalues for gauge theories with fermions, providing a general framework and specific examples for QCD-like theories without relying on Random Matrix Theory.

Contribution

It introduces a general method to relate Dirac eigenvalue distributions to density and correlation functions, applicable to various gauge theories.

Findings

Derived distributions for lowest-lying eigenvalues in QCD-like theories

Established relations valid for any gauge theory with fermions under certain conditions

Provided explicit examples without using Random Matrix Theory

Abstract

The distribution of individual Dirac eigenvalues is derived by relating them to the density and higher eigenvalue correlation functions. The relations are general and hold for any gauge theory coupled to fermions under certain conditions which are stated. As a special case, we give examples of the lowest-lying eigenvalue distributions for QCD-like gauge theories without making use of earlier results based on the relation to Random Matrix Theory.