Abstract
We consider (continuum) mass ratios of the lightest ‘glueballs’ as a function of N for SO(N) and SU(N) lattice gauge theories in D=2+1. We observe that the leading large N correction is usually sufficient to describe the N-dependence of SO(N≥3) and 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) and 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) and SU(N′) theories and the equivalence of SO(∞) and SU(∞). The same argument for a weak N-dependence can in principle apply to SU(N) and SO(N) gauge theories in D=3+1.
Highlights
Large NIn SU(N) gauge theories all-order diagrammatic arguments [1], supported by non-perturbative lattice calculations (see [9] for recent reviews), suggest that a mass ratio will approach its
(Lie algebra) equivalence between some of the theories
SU(N) and SO(2N) gauge theories are related by an orbifold projection [11], and it can be shown that this implies an identical common particle spectrum at N = ∞ [12]
Summary
In SU(N) gauge theories all-order diagrammatic arguments [1], supported by non-perturbative lattice calculations (see [9] for recent reviews), suggest that a mass ratio will approach its. One can show that the leading planar diagrams are the same in both cases up to a factor of 2 in g2 [10]. SU(N) and SO(2N) gauge theories are related by an orbifold projection [11], and it can be shown that this implies an identical common particle spectrum at N = ∞ [12]. We can expect identical mass spectra at N = ∞, i.e. in the common C = + sector of the two theories
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