Barak Bringoltz

We calculate energies and tensions of closed k-strings in (2+1)-dimensional SU(N) gauge theories with N=4,5,6,8. When we study the dependence of the ground state energy on the string length, we find that it is well described by a Nambu-Goto (NG) free bosonic string for large lengths. At shorter lengths we see deviations which we fit, and this allows us to control the systematic error involved in extracting the tension. We compare the resulting string tensions with Casimir scaling, which we find to be lower than our data by 1%-4%. Extrapolating our results to N=oo we see that our data fits more naturally to 1/N rather than 1/N^2 corrections. Finally, we see that the full spectrum of the k-string states falls into sectors that belong to particular irreducible representations of SU(N).

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.