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

Abstract

The ratios between string tensions $σ_D$ of color-electric flux tubes in higher and fundamental SU(3) representations, $d_{D} \equiv σ_{D}/σ_{\bf 3}$, are systematically studied in a Weyl symmetric formulation of the DGL theory. The ratio is found to depend on the Ginzburg-Landau (GL) parameter, $κ\equiv m_χ/m_{B}$, the mass ratio between monopoles ($m_χ$) and dual gauge bosons ($m_{B}$). While the ratios $d_{D}$ 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 $d_{D}$ observed in lattice QCD simulations.