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The k-string tensions are explored in the 4-d $[U(1)]^{N-1}$-invariant dualAbelian-Higgs-type theory. In the London limit of this theory, the Casimirscaling is found in the approximation when small-sized closed dual strings aredisregarded. When these strings are treated in the dilute-plasma approximation,explicit corrections to the Casimir scaling are found. The leading correctiondue to the deviation from the London limit is also derived. Its N-alitydependence turns out to be the same as that of the first non-trivial correctionproduced by closed strings. It also turns out that this N-ality dependencecoincides with that of the leading correction to the k-string tension, whichemerges by way of the non-diluteness of the monopole plasma in the 3-d SU(N)Georgi-Glashow model. Finally, we prove that, in the latter model, Casimirscaling holds even at monopole densities close to the mean one, provided thestring world sheet is flat.Comment: 21 pages, no figures, uses JHEP3.cl

k-string tensions in the 4-d SU(N)-inspired dual Abelian-Higgs-type theory