Weyl invariant formulation of the flux-tube solution in the dual Ginzburg-Landau theory

The flux-tube solution in the dual Ginzburg-Landau (DGL) theory in the Bogomol'nyi limit is studied by using the manifestly Weyl invariant form of the DGL Lagrangian. The dual gauge symmetry is extended to $[\mathrm{U}(1){]}_{m}^{3},$ and, accordingly, there appear three different types of flux tube. The string tension for each flux tube is calculated analytically and is found to be the same owing to Weyl symmetry. It is suggested that the manifestly Weyl invariant approach enables us to treat flux tubes of various types in the DGL theory in a framework quite similar to the $\mathrm{U}(1)$ dual Abelian Higgs theory.

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