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