Effective string action for the U(1)xU(1) dual Ginzburg-Landau theory beyond the London limit

The effective string action of the color-electric flux tube in the U(1) x U(1) dual Ginzburg-Landau (DGL) theory is studied by performing a path-integral analysis by taking into accountthe finite thickness of the flux tube. The DGL theory, corresponding to the low-energy effective theory of Abelian-projected SU(3) gluodynamics, can be expressed as s [U(1)]^{3} dual Abelian Higgs (DAH) model with a certain constraint in the Weyl symmetric formulation. This formulation allows us to adopt quite similar path-integral techniques as in the U(1) DAH model, and therefore, the resulting effective string action in the U(1) x U(1) DGL theory has also quite a similar structure except the number of color degrees of freedom. A modified Yukawa interaction appears as a boundary contribution, which is completely due to the finite thickness of the flux tube, and is reduced into the ordinary Yukawa interaction in the deep type-II (London) Limit.