Kosterlitz-Thouless transition on the worldsheet of the QCD string

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 Lüscher-Weisz effective string action for the flux-tube energy levels at finite L⊥. As the size of one transverse dimension is varied, we predict a Kosterlitz-Thouless transition of the worldsheet field theory at σ(L⊥)L⊥ ≃ 1/8π 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.