Glueball masses and other physical properties of SU(N) gauge theories in D=3+1: a review of lattice results for theorists

TL;DR

This review compiles lattice QCD results for continuum SU($N$) gauge theories in 3+1 dimensions, focusing on the glueball spectrum, confinement scale, deconfinement temperature, topological susceptibility, running-scale parameters, and the $r_0$ scale. It presents continuum-extrapolated results for SU(2) and SU(3) and discusses trends toward the large-$N$ limit, including preliminary SU(4) data and analyses suggesting a smooth large-$N$ behavior with $g^2$ scaling as $1/N$. The work highlights methodological issues in lattice spacing, spin identification, and finite-volume effects, and emphasizes the need for more precise SU(4) calculations to firmly establish large-$N$ extrapolations and the universality of the confining string. Overall, lattice results provide essential benchmarks for analytic approaches to non-perturbative gauge dynamics and guide future improvements in lattice actions and techniques.

Abstract

We summarise what lattice simulations have to say about the physical properties of continuum SU(N) gauge theories in 3+1 dimensions. The quantities covered are: the glueball mass spectrum, the confining string tension, the temperature at which the theory becomes deconfined, the topological susceptibility, the value of the scale Lambda{MS-bar} that governs the rate at which the coupling runs and the r0 parameter that characterises the static quark potential at intermediate distances.