Casimir scaling in a dual superconducting scenario of confinement

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The string tensions of flux tubes associated with static charges in various SU(3) representations are studied within the dual Ginzburg-Landau (DGL) theory. The ratios of the string tensions between higher and fundamental representations, dD ≡ σD/σF, are found to depend only on the Ginzburg-Landau (GL) parameter, κ= mχ/mB, the mass ratio between monopoles mχ and dual gauge bosons mB. In the case of the Bogomol'nyi limit (κ=1), analytical values of dD are easily obtained by adopting the manifestly Weyl invariant formulation of the DGL theory, which are provided simply by the number of color-electric Dirac strings inside the flux tube. A numerical investigation of the ratio for various GL-parameter cases is also performed, which suggests that the Casimir scaling is obtained in the type-II parameter range within the interval κ=5 9 for various ratios dD.