Eigenvalue Distributions in Yang-Mills Integrals

TL;DR

This paper analyzes eigenvalue distributions in SU(N) Yang-Mills integrals, establishing convergence conditions, comparing with Monte Carlo results, and revealing distinct spectral density behaviors in bosonic and supersymmetric models across various dimensions.

Contribution

It introduces new convergence criteria for correlation functions in Yang-Mills integrals and characterizes the eigenvalue distributions, including their asymptotic behaviors, with comparisons to non-perturbative calculations.

Findings

Convergence conditions match Monte Carlo results across gauge groups and dimensions.

Bosonic models have moments of all orders as N approaches infinity.

Supersymmetric models exhibit eigenvalue distributions with power-law tails independent of N.

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.