SU(N) gauge theories in 2+1 dimensions -: art. no. 014512

We calculate the mass spectra and string tensions of SU(2), SU(3), SU(4) and SU(5) gauge theories in 2+1 dimensions. We do so by simulating the corresponding lattice theories and then extrapolating dimensionless mass ratios to the continuum limit. We find that such mass ratios are, to a first approximation, independent of the number of colors, N-c, and that the remaining dependence can be accurately reproduced by a simple O(1/N-c(2)) correction. This provides us with a prediction of these mass ratios for all SU(N-c) theories in 2+1 dimensions and demonstrates that these theories are already "close" to N-c=infinity for N(c)greater than or equal to 2. We find that the theory retains a non-zero confining string tension as N-c-->infinity and that the dimensionful coupling g(2) is proportional to 1/N-c at large N-c, when expressed in units of the dynamical length scale of the theory. During the course of these calculations we study in detail the effects of including over-relaxation in the Monte Carlo calculation, of using a mean-held improved coupling to extrapolate to the continuum limit, and the use of space-time asymmetric lattice actions to resolve heavy glueball correlators. [S0556-2821(98)03423-3].