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=∞ we find that there remains a discrepancy of ≃1%, which is a convincing ∼6σ effect. Thus, while the Karabali-Nair analysis is remarkably accurate at N=∞, it is not exact.