Su(N) gauge theories in four dimensions: Exploring the approach to n = ∞

Abstract

We calculate the string tension, σ, and some of the lightest glueball masses, mG, in 3 + 1-dimensional SU(N) lattice gauge theories for 2 ≤ N ≤ 5. From the√continuum extrapolation of the lattice values, we find that the mass ratios mG/σ 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/N2) correction. We confirm that the smooth large-N limit we find, is obtained by keeping a constant ’t Hooft coupling. We also calculate 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.