The Microscopic Spectral Density of the QCD Dirac Operator

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.