We consider whether the 1/N corrections to k-string tensions must begin at
order 1/N^2, as in the Sine Law, or whether odd powers of 1/N, as in Casimir
Scaling, are also acceptable. The issue is important because different models
of confinement differ in their predictions for the representation-dependence of
k-string tensions, and corrections involving odd powers of 1/N would seem to be
ruled out by the large-N expansion. We show, however, that k-string tensions
may, in fact, have leading 1/N corrections, and consistency with the large-N
expansion, in the open string sector, is achieved by an exact pairwise
cancellation among terms involving odd powers of 1/N in particular combinations
of Wilson loops. It is shown how these cancellations come about in a concrete
example, namely, strong coupling lattice gauge theory with the heat-kernel
action, in which k-string tensions follow the Casimir scaling rule.Comment: Talk presented at the XXIX International Symposium on Lattice Field
Theory - Lattice 2011, July 10-16, 2011, Squaw Valley, Lake Tahoe, Californi