SU(N)gauge theories in 2+1 dimensions

Abstract

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 $\mathrm{SU}{(N}_{c})$ theories in 2+1 dimensions and demonstrates that these theories are already ``close'' to ${N}_{c}=\ensuremath{\infty}$ for ${N}_{c}>~2.$ We find that the theory retains a non-zero confining string tension as ${N}_{c}\ensuremath{\rightarrow}\ensuremath{\infty}$ 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-field improved coupling to extrapolate to the continuum limit, and the use of space-time asymmetric lattice actions to resolve heavy glueball correlators.