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 or and the low-energy constants c(k) of the theory are arbitrary functions of the sizes of the transverse dimensions L-perpendicular to. 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-perpendicular to, given sigma (L-perpendicular to) and c(k)(L-perpendicular to). The Luscher 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-perpendicular to. As the size of one transverse dimension is varied, we predict a Kosterlitz-Thouless transition of the worldsheet field theory at or (L-perpendicular to)L-perpendicular to(2) similar or equal to 1/87 pi 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. (c) 2005 Elsevier B.V. All rights reserved.