String tensions of SU(N) gauge theories in 2+1 dimensions

Abstract

We calculate the energy spectrum of closed strings in SU(N) gauge theories with N=2,3,4,6,8 in 2+1 dimensions to a high accuracy. We attempt to control all systematic errors, and this allows us to perform a precise comparison with different theoretical predictions. When we study the dependence of the string mass on its length L we find that the Nambu-Goto prediction is a very good approximation down to relatively short lengths, where the Luscher term alone is insufficient. We then isolate the corrections to the Luscher term, and compare them to recent theoretical predictions, which indeed seem to be mildly preferred by the data. When we take these corrections into account and extract string tensions from the string masses, we find that their continuum limit is lower by 2%-1% from the predictions of Karabli, Kim, and Nair. The discrepancy decreases with N, but when we extrapolate our results to N=oo we still find a discrepancy of 0.88% which is a 4.5 sigma effect.