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In the context of four-dimensional SU(N) gauge theories, we study thespectrum of the confining strings. We compute, for the SU(6) gauge theoryformulated on a lattice, the three independent string tensions sigma_k relatedto 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 consistentwith the sine formula sigma_k/sigma = sin(k pi/N) / \sin(pi/N) for the ratiobetween sigma_k and the standard string tension sigma, and show deviations fromthe Casimir scaling.  The sine formula is known to emerge in supersymmetric SU(N) gauge theoriesand in M-theory. We comment on an analogous behavior exhibited bytwo-dimensional SU(N)xSU(N) chiral models.Comment: version accepted for publication in Phys Rev D (Rap Comm

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

<i>k</i>-string tensions in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="normal">SU</mml:mi><mml:mn /><mml:mo>(</mml:mo><mml:mi>N</mml:mi><mml:mo>)</mml:mo><mml:mn /></mml:math>gauge theories

k-string tensions inSU(N)gauge theories