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We study the spectrum of closed flux tubes in four dimensional SU(N) gaugetheories. We do so by calculating the energies of the low lying states with thevariational technique (whose basis consists of about ~700 operators). We studystates of different values of angular momentum, transversal parity,longitudinal parity, and longitudinal momentum, and compare the results witheffective string theories (ESTs) such as the Nambu-Goto (NG) model. Most of ourstates agree very well with the Nambu-Goto predictions and since most of ourflux-tubes' lengths are outside the radius of convergence of the ESTs, then forsome states it is only the NG that predicts the spectrum well. This stronglysuggests that the ESTs can be re-summed. Nonetheless, there are a few states(all with negative parity and in the same representation of the latticerotation group) that exhibit large deviations from the NG predictions; thesedeviations might provide clues to the nature of the effective string theorydescribing the large-N QCD string.

The spectrum of closed loops of fundamental flux in D = 3+1 SU(N) gauge theories