Closed flux tubes and their string description in D=2+1 SU(N) gauge theories

We carry out lattice calculations of the spectrum of confining flux tubes that wind around a spatial torus of variable length l, in 2 + 1 dimensions. We compare the energies of the lowest ∼30 states to the free string Nambu-Goto model and to recent results on the universal properties of effective string actions. Our most useful calculations are in SU(6) at a small lattice spacing, which we check is very close to the N → ∞ continuum limit. We find that the energies, E n (l), are remarkably close to the predictions of the free string Nambu-Goto model, even well below the critical length at which the expansion of the Nambu-Goto energy in powers of 1/l 2 diverges and the series needs to be resummed. Our analysis of the ground state supports the universality of the O(1/l) and the O(1/l 3) corrections to σl, and we find that the deviations from Nambu-Goto at small l prefer a leading correction that is O(1/l 7), consistent with theoretical expectations. We find that the low-lying states that contain a single phonon excitation are also consistent with the leading O(1/l 7) correction dominating down to the smallest values of l. By contrast our analysis of the other light excited states clearly shows that for these states the corrections at smaller l resum to a much smaller effective power. Finally, and in contrast to our recent calculations in D = 3 + 1, we find no evidence for the presence of any non-stringy states that could indicate the excitation of massive flux tube modes.