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

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 = ∞. I describe calculations of the low-lying ‘glueball’ mass spectrum, of the string tensions of k-strings and of topological fluctuations for 2 ≤ N ≤ 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/ N 2) 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 it is consistent, within quite small errors, with either the M(-theory)QCD-inspired conjecture that σ k ∝ sin(π k/N) 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 = ∞ limit.