Distribution of the k-th smallest Dirac operator eigenvalue

TL;DR

This paper derives the probability distribution of the k-th smallest eigenvalue of the Dirac operator in QCD and related theories using Random Matrix Theory, providing insights into spectral properties in finite-volume regimes.

Contribution

It introduces an exact derivation of the eigenvalue distribution leveraging Random Matrix Theory, applicable to finite-volume QCD and gauge theories.

Findings

Exact distribution formulas for Dirac eigenvalues

Application to finite-volume QCD spectral analysis

Enhanced understanding of eigenvalue statistics in gauge theories

Abstract

Based on the exact relationship to Random Matrix Theory, we derive the probability distribution of the k-th smallest Dirac operator eigenvalue in the microscopic finite-volume scaling regime of QCD and related gauge theories.