Abstract
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, ${d}_{D}\ensuremath{\equiv}{\ensuremath{\sigma}}_{D}/{\ensuremath{\sigma}}_{F},$ are found to depend only on the Ginzburg-Landau (GL) parameter, $\ensuremath{\kappa}{=m}_{\ensuremath{\chi}}{/m}_{B},$ the mass ratio between monopoles ${m}_{\ensuremath{\chi}}$ and dual gauge bosons ${m}_{B}.$ In the case of the Bogomol'nyi limit $(\ensuremath{\kappa}=1),$ analytical values of ${d}_{D}$ 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 $\ensuremath{\kappa}=5\ensuremath{\sim}9$ for various ratios ${d}_{D}.$
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