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

TL;DR

This paper investigates the N-dependence of glueball mass ratios in 2+1 dimensional SO(N) and SU(N) gauge theories, finding that the leading large N correction is sufficient and that the correction coefficient is unusually small, possibly due to Lie algebra constraints.

Contribution

It demonstrates that the N-dependence of mass ratios is weak and that the correction coefficients are anomalously small, linking this to Lie algebra equivalences between theories.

Findings

Leading large N correction describes N-dependence well.

Correction coefficients are anomalously small.

Weak N-dependence may follow from Lie algebra constraints.

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.geq.3) and SU(N.geq.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(infinity) and SU(infinity). The same argument for a weak N-dependence can in principle apply to SU(N) and SO(N) gauge theories in D=3+1.