  We investigate the properties of the QCD string in the Euclidean SU(N) pure
gauge theory when the space-time dimensions transverse to it are periodic. We
propose a generalisation of the Luscher-Weisz effective string action for the
flux-tube energy levels at finite L_perp. As the size of one transverse
dimension is varied, we predict a Kosterlitz-Thouless transition of the
worldsheet field theory driven by vortices, after which the periodic component
of the worldsheet displacement vector develops a mass gap and the effective
central charge drops by one unit. The universal properties of the transition
are emphasized.
