On the weak N -dependence of SO(N)SO(N) and SU(N)SU(N) gauge theories in 2+12+1 dimensions

We consider (continuum) mass ratios of the lightest ‘glueballs’ as a function of N   for SO(N)SO(N) and SU(N)SU(N) lattice gauge theories in D=2+1D=2+1. We observe that the leading large N correction is usually sufficient to describe the N  -dependence of SO(N≥3)SO(N≥3) and SU(N≥2)SU(N≥2), within the errors of the numerical calculation. Just as interesting is the fact that the coefficient of this correction almost invariably turns out to be anomalously small, for both SO(N)SO(N) and SU(N)SU(N). We point out that this can follow naturally from the strong constraints that one naively expects from the Lie algebra equivalence between certain SO(N)SO(N) and SU(N′)SU(N′) theories and the equivalence of SO(∞)SO(∞) and SU(∞)SU(∞). The same argument for a weak N  -dependence can in principle apply to SU(N)SU(N) and SO(N)SO(N) gauge theories in D=3+1D=3+1.