Topological term in the string representation of the Wilson loop in the dilute instanton gas approximation

Antonov, Dmitri; Эберт, Д.

doi:10.1103/physrevd.58.067901

Cited by 18 publications

(60 citation statements)

References 29 publications

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“…The aim of the present Letter is to extend the results of Ref. [6] to the case of Abelian-projected SU (3)-gluodynamics in 2+1 dimensions and finally to emphasize confinement in this theory in the sense of the Wilson area law [8].…”

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confidence: 99%

“…Indeed, this assumption leads to an effective Ginzburg-Landau type theory [3], whose string representation can further be investigated [4] analogously to that of the usual dual superconductor [5]. On the other hand, recently string representation of the Abelian-projected SU (2)-gluodynamics has been derived [6] under a weaker assumption, which states that Abelian-projected monopoles form a gas, rather than condense into the dual Higgs field. Such a way of treating Abelianprojected monopoles in the SU (2)-gluodynamics makes the string representation of the Wilson loop in this theory (which describes an external test particle, electrically charged w.r.t.…”

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Confining strings in the Abelian-projected SU (3)-gluodynamics

Antonov

2000

Europhys. Lett.

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Abstract. -String representation of the Wilson loop in 3D Abelian-projected SU (3)-gluodynamics is constructed in the approximation that Abelian-projected monopoles form a gas. Such an assumption is much weaker than the standard one, demanding the monopole condensation. It is demonstrated that the summation over world sheets, bounded by the contour of the Wilson loop, is realized by the summation over branches of a certain effective multivalued potential of the monopole densities. Finally, by virtue of the so-constructed representation of the Wilson loop in terms of the monopole densities, this quantity is evaluated in the approximation of a dilute monopole gas, which makes confinement in the model under study manifest.On the way of constructing the string representation of SU (3)-gluodynamics by means of the method of Abelian projections [1] (see Ref.[2] for recent reviews), the main results have up to now been obtained under the assumption of the monopole condensation. Indeed, this assumption leads to an effective Ginzburg-Landau type theory [3], whose string representation can further be investigated [4] analogously to that of the usual dual superconductor [5]. On the other hand, recently string representation of the Abelian-projected SU (2)-gluodynamics has been derived [6] under a weaker assumption, which states that Abelian-projected monopoles form a gas, rather than condense into the dual Higgs field. Such a way of treating Abelianprojected monopoles in the SU (2)-gluodynamics makes the string representation of the Wilson loop in this theory (which describes an external test particle, electrically charged w.r.t. the U (1) Cartan subgroup of SU (2)) similar to that of the Wilson loop in compact QED [7]. The aim of the present Letter is to extend the results of Ref.[6] to the case of Abelian-projected SU (3)-gluodynamics in 2+1 dimensions and finally to emphasize confinement in this theory in the sense of the Wilson area law [8].Let us start our analysis with considering the pure monopole contribution to the action of this theory, keeping for a while aside the noncompact part of diagonal fields. (The off-diagonal fields are as usual disregarded on the basis of the so-called Abelian dominance hypothesis [9]. That is because they are argued to become very massive (and thus short-ranged) and therefore c EDP Sciences

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Confining strings in the Abelian-projected SU (3)-gluodynamics

Antonov

2000

Europhys. Lett.

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“…In particular, in the string limit of QCD, studied in Refs. [5][6][7], when T g → 0 while the value of the string tension is kept fixed, m corresponds to D QCD (0) σ . Moreover, the short distance asymptotic behaviours (27) and (28) are also in line with the results obtained within the SVM of QCD in the lowest order of perturbation theory.…”

Section: String Representation For the Generating Functional Of Fieldmentioning

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String representation of field correlators in the Dual Abelian Higgs Model

Antonov

Эберт

1999

Eur. Phys. J. C

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By making use of the path integral duality transformation, we derive the string representation for the partition function of an extended Dual Abelian Higgs Model containing gauge fields of external currents of electrically charged particles. By the same method, we obtain the corresponding representations for the generating functionals of gauge field and monopole current correlators. In the case of bilocal correlators, the obtained results are found to be in agreement with the dual Meissner scenario of confinement and with the Stochastic Model of the QCD

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“…The SU(3) string in an abelian projection may be considered as a composite [11,12] of the three elementary strings with the winding numbers n i of the Higgs fields χ i subjected to relation (5). The phase of the Higgs field must be singular at the center of the elementary string with non-zero winding number n i .…”

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Classical string solutions in effective infrared theory of SU(3) gluodynamics

Chernodub

2000

Physics Letters B

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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 superconductors (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.

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Topological term in the string representation of the Wilson loop in the dilute instanton gas approximation

Cited by 18 publications

References 29 publications

Confining strings in the Abelian-projected SU (3)-gluodynamics

Confining strings in the Abelian-projected SU (3)-gluodynamics

String representation of field correlators in the Dual Abelian Higgs Model

Classical string solutions in effective infrared theory of SU(3) gluodynamics

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