The Microscopic Spectral Density of the QCD Dirac Operator

TL;DR

This paper derives the microscopic spectral density of the Dirac operator in SU(N_c) Yang-Mills theory with fundamental fermions, confirming results with Random Matrix Theory through supermanifold integration techniques.

Contribution

It introduces an exact supermanifold integral method to compute the spectral density, aligning field theory results with Random Matrix Theory predictions.

Findings

Exact expression for spectral density in SU(N_c) Yang-Mills

Agreement with Random Matrix Theory calculations

Method applicable to theories with fundamental fermions

Abstract

We derive the microscopic spectral density of the Dirac operator in $SU(N_c\geq 3)$ Yang-Mills theory coupled to $N_f$ fermions in the fundamental representation. An essential technical ingredient is an exact rewriting of this density in terms of integrations over the super Riemannian manifold $Gl(N_f+1|1)$. The result agrees exactly with earlier calculations based on Random Matrix Theory.