SU(N) gauge theories in 3+1 dimensions: glueball spectrum, string tensions and topology

We calculate the low-lying glueball spectra, some string tensions and some properties of topology and the running coupling for SU(N) lattice gauge theories in 3+1 dimensions, for N=2 to N=12, and for glueball states in all the representations of the cubic rotation group, as well as P and C. We extrapolate these results to the continuum limit of each theory and then to N=oo. For a number of these states we are able to identify their continuum spins with very little ambiguity. We calculate the fundamental string tension and k=2 string tension and investigate the N dependence of the ratio. Using the string tension as the scale, we confirm that g(a)**2 varies as 1/N for constant physics at large N. We fit our calculated values of the string tension with the 3-loop beta-function, and extract a value for Lambda-MSbar, in units of the string tension, for all our values of N, including SU(3). We provide analytic formulae for estimating the string tension at a given lattice coupling. We calculate the topological charge Q for N less than or equal to 6, where it fluctuates sufficiently for a plausible estimate of the continuum topological susceptibility. We also calculate the renormalisation of the lattice topological charge, ZQ(beta), for all our SU(N) gauge theories, using a standard definition of the charge, and we provide interpolating formulae, which may be useful in estimating the renormalisation of the lattice theta parameter. We provide quantitative results for how the topological charge `freezes' with decreasing lattice spacing and with increasing N. Although we are able to show that within our typical errors our glueball and string tension results are insensitive to the freezing of Q at larger N and beta, we choose to perform our calculations with a typical distribution of Q imposed upon the fields so as to further reduce any potential systematic errors.