Curvature Expansion for the Background-Induced Gluodynamics String

Antonov, Dmitri; Эберт, Д.; Simonov, Yu. A.

doi:10.1142/s0217732396001910

Cited by 39 publications

(67 citation statements)

References 9 publications

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“…(16) is taken w.r.t. the monopole partition function (2), we can apply to this equation the same procedure, which led to the representation (12)- (13). In this way, we conclude that the monopole contribution to the Wilson loop (14) is given by the following expression:…”

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confidence: 87%

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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confidence: 87%

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

Antonov

2000

Europhys. Lett.

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“…Here, it has been naturally assumed that the vortex loops of different kinds have the same fugacity ζ ∝ e −S 0 , since different θ sing. a 's enter the initial partition function (28) in the symmetric way. Clearly, the action S 0 of a single loop can be estimated analogously to how it has been done in the previous Subsection for the SU(2)-case.…”

Section: Su (3)-casementioning

confidence: 99%

Field correlators in Abelian-projected theories and stochastic vacuum model

Antonov

2000

J. High Energy Phys.

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The bilocal electric field strength correlators in Abelian-projected SU(2)-and SU(3)-theories are derived with accounting for the contributions to these quantities brought about by the virtual vortex loops, built out of the dual Nielsen-Olesen strings. Owing to the screening of magnetic charge of the dual vector bosons in the gas of such loops, these bosons become heavier, which leads to the respective change of the correlation length of the vacuum in the models under study. Besides that, it turns out that such a screening leads also to the appearance of the long-range contribution to one of the two coefficient functions, which parametrize the bilocal correlator within the Stochastic Vacuum Model. Finally, the modifications of the propagators of the dual vector bosons, inspired by the correlation effects in the gas of vortex loops, are also discussed.

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“…One can parametrize the world volume of the membrane, S, by the vector x µ (ξ), ξ = (ξ 1 , ξ 2 , ξ 3 ), and expand the above-mentioned term in powers of the derivatives ∂ a ≡ ∂/∂ξ a supplied with the appropriate powers of m in the denominator. Such an expansion is similar to the analogous expansion of non-local string effective actions [6,4], and its first three leading terms have the following form:…”

Section: Confining Membranesmentioning

confidence: 87%

Confining membranes and dimensional reduction

Antonov¹

2001

J. High Energy Phys.

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The dual theory describing the 4D Coulomb gas of point-like magnetically charged objects, which confines closed electric strings, is considered. The respective generalization of the theory of confining strings to confining membranes is further constructed. The same is done for the analogous SU(3)-inspired model. We then consider a combined model which confines both electric charges and closed strings. Such a model is nothing, but the mixture of the above-mentioned Coulomb gas with the condensate of the dual Higgs field, described by the dual Abelian Higgs model. It is demonstrated that in a certain limit of this dual Abelian Higgs model, the system under study undergoes naively the dimensional reduction and becomes described by the (completely integrable) 2D sine-Gordon theory. In particular, owing to this fact, the phase transition in such a model must be of the Berezinskii-Kosterlitz-Thouless type, and the respective critical temperature is expressed in terms of the parameters of the dual Abelian Higgs model. However, it is finally discussed that the dimensional reduction is rigorously valid only in the strong coupling limit of the original 4D Coulomb gas. In such a limit, this reduction transforms the combined model to the 2D free bosonic theory. *

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Curvature Expansion for the Background-Induced Gluodynamics String

Cited by 39 publications

References 9 publications

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

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

Field correlators in Abelian-projected theories and stochastic vacuum model

Confining membranes and dimensional reduction

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