k-string tensions in SU(N) gauge theories

In the context of four-dimensional SU(N) gauge theories, we study the spectrum of the confining strings. We compute, for the SU(6) gauge theory formulated on a lattice, the three independent string tensions sigma_k related to sources with Z_N charge k=1,2,3, using Monte Carlo simulations. Our results, whose uncertainty is approximately 2% for k=2 and 4% for k=3, are consistent with the sine formula sigma_k/sigma = sin(k pi/N) / \sin(pi/N) for the ratio between sigma_k and the standard string tension sigma, and show deviations from the Casimir scaling. The sine formula is known to emerge in supersymmetric SU(N) gauge theories and in M-theory. We comment on an analogous behavior exhibited by two-dimensional SU(N)xSU(N) chiral models.