Center vortices and k-strings

The vortex contribution to the k-string tensions is computed for SU(N) gauge theories. We deduce the surface densities of vortices, needed to reproduce the sine scaling and the Casimir scaling formulae, recently obtained from numerical simulations on the lattice. We find that such densities need to grow linearly in N. The naive picture of the QCD vacuum as a dilute gas of vortices is therefore incapable of reproducing the physics of confinement for large N.