A precise calculation of the fundamental string tension in SU(N) gauge theories in 2+1 dimensions

We use lattice techniques to calculate the continuum string tensions of SU(N) gauge theories in 2 + 1 dimensions. We attempt to control all systematic errors at a level that allows us to perform a precise test of the analytic prediction of Karabali, Kim and Nair. We find that their prediction is within 3% of our values for all N and that the discrepancy decreases with increasing N. When we extrapolate our results to N = infinity we find that there remains a discrepancy of similar or equal to 1%, which is a convincing similar to 6 sigma effect. Thus, while the Karabali-Nair analysis is remarkably accurate at N = infinity, it is not exact. (c) 2006 Elsevier B.V. All rights reserved.