Confinement and the effective string theory in SU(N- > oo) : a lattice study.

We calculate in the SU(6) gauge theory the mass of the lightest flux loopthat winds around a spatial torus, as a function of the torus size, taking careto achieve control of the main systematic errors. For comparison we perform asimilar calculation in SU(4). We demonstrate approximate linear confinement andshow that the leading correction is consistent with what one expects if theflux tube behaves like a simple bosonic string at long distances. We obtainsimilar but less accurate results for stable (k-)strings in higherrepresentations. We find some evidence that for k>1 the length scale at whichthe bosonic string correction becomes dominant increases as N increases. Weperform all these calculations not just for long strings, up to about 2.5`fm'in length, but also for shorter strings, down to the minimum length, lc = 1/Tc,where Tc is the deconfining temperature. We find that the mass of theground-state string, at all length scales, is not very far from the simpleNambu-Goto string theory prediction, and that the fit improves as N increasesfrom N=4 to N=6. We estimate the mass of the first excited string and find thatit also follows the Nambu-Goto prediction, albeit more qualitatively. Wecomment upon the significance of these results for the string description ofSU(N) gauge theories in the limit of infinite N.Comment: 21 pages, 5 figure