k-String Tension and the 1/N Expansion
I will address the question of whether the large-N expansion of the k-string tension in pure SU(N) gauge theories must contain only even powers of 1/N (as in the sine law), or whether odd-power contributions can also appear (as in Casimir scaling). A simple argument would suggest that, since the Wilson loops in the reducible tensorial representation contain only even powers of 1/N, the same should be true for the k-string tension. I will show that this argument is not correct and in general 1/N corrections are expected. The cancellation of the odd powers in 1/N for the tensorial reducible representation is nontrivial, and it is generated by very different mechanisms in the open and closed string channels. I will substantiate this picture with a computation in the framework of the strong-coupling expansion for the lattice-discretized theory and I will discuss what results are expected to be valid in the continuum limit.