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

TL;DR

This paper uses a matrix model to estimate low-lying glueball energies in pure Yang-Mills theory, deriving an RG equation for the coupling and predicting glueball masses consistent with lattice results.

Contribution

It introduces a variational matrix model approach to approximate Yang-Mills glueball spectra and derives an RG equation for the coupling based on ground state energy fixing.

Findings

Glueball mass estimates agree with lattice simulations

Derived RG equation for Yang-Mills coupling as a function of sphere radius

Provided a variational method for low-energy spectrum approximation

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.