String Representation of the Dual Ginzburg-landau Theory beyond the London Limit

The effective string action of the color-electric flux tube in the dual Ginzburg-Landau (DGL) theory is studied by performing a path-integral analysis by taking into account the finite thickness of the flux tube. A modified Yukawa interaction appears as a boundary contribution and is reduced into the ordinary Yukawa interaction in the London Limit. The dual Ginzburg-Landau (DGL) theory can sketch the dual superconductor scenario of quark confinement mechanism intuitively by the formation of a flux tube due to the dual Meissner effect. Since the flux tube corresponds to the hadronic object, the construction of the effective string action of the flux tube is one of the interesting applications of the DGL theory to the hadron physics. In this brief report, we discuss the structure of the effective string action of the U(1) version of the DGL theory by using path-integral analysis.[1] In particular, we pay attention to the effect of the finite thickness of the flux tube to the form of the string action. The U(1) DGL action in the differential form has the following form: SDGL = βg 2 (F ) + ((d− iB)χ∗, (d + iB)χ) + λ(|χ|2 − v), (1) where B is the dual gauge field (1-form) and χ = φ exp(iη) (φ, η ∈ <) the complex-scalar monopole field (0-form). The dual gauge coupling, the strength of the self-coupling and the monopole condensate are denoted by βg = 1/g, λ and v, respectively. They are related to the two mass scales of the theory: the mass of the dual gauge field mB = √ 2 gv and that of the monopole field mχ =2 √ λ v. The inverses of these masses correspond to the penetration depth and coherence length, respectively. 1Presented by M. Koma at “Confinement V”, Gargnano, Italy, 10-14 Sep. 2002