Eigenvalue Distributions in Yang-Mills Integrals

Abstract

We investigate one-matrix correlation functions for finite SU(N) Yang-Mills integrals with and without supersymmetry. We propose novel convergence conditions for these correlators which we determine from the one-loop perturbative effective action. These conditions are found to agree with non-perturbative Monte Carlo calculations for various gauge groups and dimensions. Our results yield important insights into the eigenvalue distributions rho(lambda) of these random matrix models. For the bosonic models, we find that the spectral densities rho(lambda) possess moments of all orders as N -> Infinity. In the supersymmetric case, rho(lambda) is a wide distribution with an N-independent asymptotic behavior rho(lambda) ~ lambda^(-3), lambda^(-7), lambda^(-15) for dimensions D=4,6,10, respectively.