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 fmd that the ratios of masses are, to a first approximation, independent of N-c and that the remain ing dependence can be accurately reproduced by a simple O(1/N-c(2)) co rrection. This provides us with a prediction of these mass ratios for all SU(N-c) theories in 2+1 dimensions and demonstrates that these the ories are 'close' to N-c = infinity for N-c greater than or equal to 2 . We also find that, when expressed in units of the dynamical length s cale of the theory, the dimensionful coupling g(2) is proportional to 1/N-c at large N-c. We confirm that these theories are indeed confinin g in the limit N-c --> infinity. We describe preliminary calculations in 3+1 dimensions which indicate that the same will be true there. (C) 1997 Elsevier Science B.V.