  We address the question of whether the large-N expansion in pure SU(N) gauge
theories requires that k-string tensions must have a power series expansion in
1/N^2, as in the sine law, or whether 1/N contributions are also allowable, as
in Casimir scaling. We find that k-string tensions may, in fact, have 1/N
corrections, and consistency with the large-N expansion in the open-string
sector depends crucially on an exact cancellation, which we will prove, among
terms involving odd powers of 1/N in particular combinations of Wilson loops.
It is shown how these cancellations are fulfilled, and consistency with the
large-N expansion achieved, in a concrete example, namely, strong-coupling
lattice gauge theory with the heat-kernel action. This is a model which has
both a 1/N^2 expansion and Casimir scaling of the k-string tensions. Analysis
of the closed string channel in this model confirms our conclusions, and
provides further insights into the large-N dependence of energy eigenstates and
eigenvalues.
