Glueball Spectra from a Matrix Model of Pure Yang-Mills Theory

Abstract

We present variational estimates for the low-lying energies of a simple matrix model that approximates $SU(3)$ Yang-Mills theory on a three-sphere of radius $R$. By fixing the ground state energy, we obtain the (integrated) renormalization group (RG) equation for the Yang-Mills coupling $g$ as a function of $R$. This RG equation allows to estimate the masses of other glueball states, which we find to be in excellent agreement with lattice simulations.