SU(Nc) gauge theories for all Nc 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(1Nc2) 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 g2 is proportional to 1Nc 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.