ar X iv : h ep - p h / 99 10 29 0 v 2 2 3 O ct 1 99 9 ITEP - TH - 28 / 99 Classical String Solutions in Effective Infrared

We investigate string solutions to the classical equations of motion (" classical QCD strings ") for a dual Ginzburg-Landau model corresponding to SU (3) gluodynamics in an abelian projection. For a certain relation between couplings of the model the string solutions are defined by first order differential equations. These solutions are related to vortex configurations of the Abelian Higgs model in the Bogomol'ny limit. An analytic expression for the string tension is derived and the string–string interactions are discussed. Our results imply that the vacuum of SU (3) gluodynamics is near a border between type-I and type-II dual superconductivity. 1. Last years the problem of color confinement in SU(N) Yang–Mills theories has been intensively studied in the framework of the abelian projection approach [1]. This approach is based on a partial gauge fixing which reduces the gauge symmetry from non–abelian gauge group to its (maximal) abelian subgroup. The diagonal elements of the gluon field transform under residual gauge transformations as abelian gauge fields, while the off-diagonal elements transform as abelian matter vector fields. Due to compactness of the Yang–Mills gauge group the residual abelian subgroup is also compact. This leads to appearance of abelian monopoles in the abelian gauge. According to the dual superconductor scenario [2] the color confinement may be explained at the classical level: if monopoles are condensed then a string forms between color charges. This string is an analog of the Abrikosov string [3] in a superconductor and the abelian monopoles are playing the role of the Cooper pairs. The dual superconductor mechanism has been confirmed by numerous lattice simulations of SU(2) Yang–Mills theory [4]. Moreover, the vacuum of SU(2) Yang–Mills theory in the abelian projection was shown [5] to be close to the border between type–I and type–II dual su-perconductors (masses of the monopole and the dual gauge boson are approximately the same). There are also strong numerical indications that the vacuum of SU(3) gluodynamics exhibits dual superconductor properties [6]. Analytical investigations [7] of the string configurations in a non–abelian dual superconductor model of SU(3) gluodynamics shows that the dual vacuum is close to the border between type-I and type-II superconductivity. In Ref. [8] similar conclusion has been derived where the SU(3) confining string was related to the Abrikosov–Nielsen–Olesen classical string solution [3, 9] in the U(1) Higgs model.