Vortices 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. From the point of view of an effective string theory, the string tension σ and the low-energy constants ck of the theory are arbitrary functions of the sizes of the transverse dimensions L⊥. Since the gauge theory is linearly confining in D=2,3 and 4 dimensions, we propose an effective string action for the flux-tube energy levels at any choice of L⊥, given σ(L⊥) and ck(L⊥). The Lüscher term only depends on the number of massless bosonic degrees of freedom and the effective theory can account for its evolution as a function of 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⊥2≃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 emphasised.