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We carry out lattice calculations of the spectrum of confining flux tubesthat wind around a spatial torus of variable length l, in 2+1 dimensions. Wecompare the energies of the lowest c.30 states to the free string Nambu-Gotomodel and to recent results on the universal properties of effective stringactions. Our most useful calculations are in SU(6) at a small lattice spacing,which we check is very close to the large-N continuum limit. We find that theenergies, En(l), are remarkably close to the predictions of the free stringNambu-Goto model, even well below the critical length at which the expansion ofthe Nambu-Goto energy in powers of 1/l diverges and the series needs to beresummed. Our analysis of the ground state supports the universality of theO(1/l) and the O(1/l^3) corrections to l.sigma, and we find that the deviationsfrom 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 statesthat contain a single phonon excitation are also consistent with the leadingO(1/l^7) correction dominating down to the smallest values of l. By contrastour analysis of the other light excited states clearly shows that for thesestates 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 noevidence for the presence of any non-stringy states that could indicate theexcitation of massive flux tube modes.

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