Glueballs, strings and topology in SU(N) gauge theory

TL;DR

This paper uses lattice methods to study continuum properties of SU(N) gauge theories, exploring how various quantities approach the large-N limit and examining the behavior of glueball masses, string tensions, and topological fluctuations across different N values.

Contribution

It provides new lattice calculations of glueball spectra, string tensions, and topological properties for N=2 to 5, demonstrating the rapid approach to large-N behavior and testing theoretical conjectures.

Findings

Mass ratios approach the large-N limit rapidly.

The k=2 string tension ratio is less than 2 and aligns with Casimir scaling.

Topological susceptibility remains finite as N approaches infinity.

Abstract

I show how one can use lattice methods to calculate various continuum properties of SU(N) gauge theories; in part to explore old ideas that N=3 might be close to N=infinity. I describe calculations of the low-lying `glueball' mass spectrum, of the string tensions of k-strings and of topological fluctuations for N=2,3,4,5. We find that mass ratios appear to show a rapid approach to the large-N limit, and, indeed, can be described all the way down to SU(2) using just a leading O(1/NxN) correction. We confirm that the smooth large-N limit we find is confining and is obtained by keeping a constant 't Hooft coupling. We find that the ratio of the k=2 string tension to the k=1 fundamental string tension is much less than the naive (unbound) value of 2 and is considerably greater than the naive bag model prediction; in fact we find that it is consistent, within quite small errors, with either the M(-theory)QCD-inspired conjecture or with `Casimir scaling'. Finally I describe calculations of the topological charge of the gauge fields. We observe that, as expected, the density of small-size instantons vanishes rapidly as N increases, while the topological susceptibility appears to have a non-zero N=infinity limit.