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 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 $N$, which in turn suggests that the vortex scenario can hardly reproduce the physics of confinement at large $N$.