Casimir scaling in a dual superconducting scenario of confinement

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, $d_D\equiv \ddot{I}{ƒ}_D/\ddot{I}{ƒ}_F$, are found to depend only on the Ginzburg-Landau (GL) parameter, $\hat{I}º=m_{\ddot{I}}‡/m_B$, the mass ratio between monopoles $m_{\ddot{I}}‡$ and dual gauge bosons $m_B$. In the case of the Bogomol'nyi limit ($\hat{I}º=1$), 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 $\hat{I}º=5\sim 9$ for various ratios $d_D$.

14 pages, 3 eps figures, RevTex. The version accepted for publication in Phys.Rev.D (Rapid Communications)