Systematics of flux tubes in the dual Ginzburg-Landau theory and Casimir scaling hypothesis: folklore and lattice facts

The ratios between string tensions σD of color-electric flux tubes in higher and fundamental SU(3) representations, dD ≡ σD/σ3, are systematically studied in a Weyl symmetric formulation of the DGL theory. The ratio is found to depend on the Ginzburg-Landau (GL) parameter, κ ≡ mχ/mB, the mass ratio between monopoles (mχ) and dual gauge bosons (mB). While the ratios dD follow a simple flux counting rule in the Bogomol’nyi limit, κ = 1.0, systematic deviations appear with increasing κ due to interactions between fundamental flux inside a higher representation flux tube. We find that in a type-II dual superconducting vacuum near κ = 3.0 this leads to a consistent description of the ratios dD observed in lattice QCD simulations.