Abstract :
We investigate the properties of the QCD string in the Euclidean image 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 image of the theory are arbitrary functions of the sizes of the transverse dimensions image. Since the gauge theory is linearly confining in image and 4 dimensions, we propose an effective string action for the flux-tube energy levels at any choice of image, given image and image. 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 image. As the size of one transverse dimension is varied, we predict a Kosterlitz–Thouless transition of the worldsheet field theory at image 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.
