  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 $\sigma$
and the low-energy constants $c_k$ of the theory are arbitrary functions of the
sizes of the transverse dimensions L_p. 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 $L_p$, given $\sigma(L_p)$ and
$c_k(L_p)$. 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 $L_p$. As the size of one transverse dimension is varied, we
predict a Kosterlitz-Thouless transition of the worldsheet field theory at
$\sigma(L_p)L_p^2 \simeq 1/8\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.
