SU(N) gauge theories in 2+1 dimensions: glueball spectra and k-string tensions

We calculate the low-lying glueball spectrum and various string tensions in SU(N) lattice gauge theories in 2+1 dimensions, and extrapolate the results to the continuum limit. We do so for for the range N=2 to N=16 so as to control the N-dependence with a useful precision. We observe a number of striking near-degeneracies in the various J^PC sectors of the glueball spectrum, in particular between C=+ and C=- states. We calculate the string tensions of flux tubes in a number of representations, and provide evidence that the leading correction to the N-dependence of the k-string tensions varies as 1/N rather than 1/N^2, and that the dominant binding of k fundamental flux tubes into a k-string is via pairwise interactions. We comment on the possible implications of our results for the dynamics of these gauge theories.