ar X iv : h ep - l at / 9 70 10 03 v 1 8 J an 1 99 7 SU ( N c ) gauge theories for all N c in 3 and 4 dimensions

We compare the mass spectra and string tensions of SU(2), SU(3) and SU(4) gauge theories in 2+1 dimensions. We find that the ratios of masses are, to a first approximation, independent of Nc and that the remaining dependence can be accurately reproduced by a simple O(1/N c ) correction. This provides us with a prediction of these mass ratios for all SU(Nc) theories in 2+1 dimensions and demonstrates that these theories are ‘close’ to Nc = ∞ for Nc ≥ 2. We also find that, when expressed in units of the dynamical length scale of the theory, the dimensionful coupling g is proportional to 1/Nc at large Nc. We confirm that these theories are indeed confining in the limit Nc → ∞. We describe preliminary calculations in 3+1 dimensions which indicate that the same will be true there. Oxford Preprint Number: OUTP–97–01P hep-lat/9701003