  We investigate the dispersion relation of the winding closed-string states in
SU(N) gauge theory defined on a d-dimensional hypertorus, in a class of
effective string theories. We show that order by order in the asymptotic
expansion, each energy eigenstate satisfies a relativistic dispersion relation.
This is illustrated in the Luscher-Weisz effective string theory to two-loop
order, where the Polyakov loop matrix elements between the vacuum and the
closed string states are obtained explicitly. We attempt a generalization of
these considerations to the case of compact dimensions transverse to the
string.
