Field correlators in Abelian-projected theories and stochastic vacuum model

Antonov, Dmitri

doi:10.1088/1126-6708/2000/07/055

Cited by 30 publications

(27 citation statements)

References 27 publications

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“…To model the grand canonical ensemble of closed strings, one can proceed along the lines of ref. [27]. Namely, one can use the fact that these strings are short-living (virtual) objects, whose typical sizes are much smaller than the typical distances between them; therefore, similarly to monopoles in the 3-d Georgi-Glashow model, closed strings form a dilute plasma.…”

Section: Corrections Due To the Higgs Field And Closed Stringsmentioning

confidence: 99%

k-string tensions in the 3-d SU(N) Georgi-Glashow model

Antonov¹,

Debbio²

2003

J. High Energy Phys.

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Abstract:The classic argument by Polyakov showing that monopoles produce confinement in the Higgs phase of the Georgi-Glashow model is generalized to study the spectrum of k-strings. We find that the leading-order low-density approximation yields Casimir scaling in the weakly-coupled 3-d SU(N ) Georgi-Glashow model. Corrections to the Casimir formula are considered. When k ∼ N , the non-diluteness effect is of the same order as the leading term, indicating that non-diluteness can significantly change the Casimir-scaling behavior. The correction produced by the propagating Higgs field is also studied and found to increase, together with the non-diluteness effect, the Casimir-scaling ratio. Furthermore, a correction due to closed k-strings is also computed and is shown to yield the same kdependence as the one due to non-diluteness, but with the opposite sign and a nontrivial N -dependence. Finally, we consider the possible implications of our analysis for the SU(N ) analogue of compact QED in four dimensions.

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Section: Corrections Due To the Higgs Field And Closed Stringsmentioning

confidence: 99%

k-string tensions in the 3-d SU(N) Georgi-Glashow model

Antonov¹,

Debbio²

2003

J. High Energy Phys.

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“…Ref. [68] for a similar situation in the plasma of closed dual strings in the Abelian-Higgs-type models]. The only thing which matters is the normalization 1 zn(τ ) = 1, that will be implied henceforth.…”

Section: Generalization To the Su(n )-Analogue Of 4d Compact Qed Withmentioning

confidence: 98%

3d Georgi–glashow Model and Confining Strings at Zero and Finite Temperatures

Antonov

Diamantini

2005

From Fields to Strings: Circumnavigating Theoretical Physics

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In this review, we discuss the confining and finite-temperature properties of the 3D SU(N ) Georgi-Glashow model, and of 4D compact QED. At zero temperature, we derive string representations of both theories, thus constructing the SU(N )-version of Polyakov's theory of confining strings. We discuss the geometric properties of confining strings, as well as the appearance of the string θ-term from the field-theoretical one in 4D, and k-string tensions at N > 2. In particular, we point out the relevance of negative stiffness for stabilizing confining strings, an effect recently re-discovered in material science. At finite temperature, we present a derivation of the confining-string free energy and show that, at the one-loop level and for a certain class of string models in the large-D limit, it matches that of QCD at large N . This crucial matching is again a consequence of the negative stiffness. In the discussion of the finite-temperature properties of the 3D Georgi-Glashow model, in order to be closer to QCD, we mostly concentrate at the effects produced by some extensions of the model by external matter fields, such as dynamical fundamental quarks or photinos, in the supersymmetric generalization of the model.

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“…Such calculations have been initially performed in various Abelian models, where confinement is provided by the monopole condensation. Those include the 3D Georgi-Glashow model and the 4D compact QED [116,117], as well as the 4D dual Abelian Higgs model in the London limit and its [U (1)] N−1 -symmetric generalization [118][119][120][121][122]. In this way, it has been explicitly shown that the vacuum correlation lengths in all these models are equal to the inverse masses of the corresponding dual vector bosons.…”

Section: Correlation Lengths Of the Stochastic Yang-mills Fieldsmentioning

confidence: 99%

World-Line Formalism: Non-Perturbative Applications

Bellettre

2016

Universe

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This review addresses the impact on various physical observables which is produced by confinement of virtual quarks and gluons at the level of the one-loop QCD diagrams. These observables include the quark condensate for various heavy flavors, the Yang-Mills running coupling with an infra-red stable fixed point, and the correlation lengths of the stochastic Yang-Mills fields. Other non-perturbative applications of the world-line formalism presented in the review are devoted to the determination of the electroweak phase-transition critical temperature, to the derivation of a semi-classical analogue of the relation between the chiral and the gluon QCD condensates, and to the calculation of the free energy of the gluon plasma in the high-temperature limit. As a complementary result, we demonstrate Casimir scaling of k-string tensions in the Gaussian ensemble of the stochastic Yang-Mills fields.Keywords: the world-line formalism; Wilson loops; analytic calculations of path integrals with the minimal-area surfaces; theoretical foundations of the stochastic vacuum model; confinement and chiral-symmetry breaking in QCD; gluonic bound states; Casimir scaling; the Yang-Mills running coupling; thermodynamics of the gluon plasma; electroweak phase transition Quark Condensate for Various Heavy FlavorsAs is well known, because of confinement in QCD, quarks and gluons do not exist as individual particles, but appear only in the form of bound states (for recent reviews, see [1,2]). The latter include mesons, baryons (as well as other possible quark bound states, such as tetra-and pentaquarks), glueballs, and the so-called hybrids consisting of a quark, an antiquark, and one or several gluons. Each bound state can be represented as an average of a certain operator over the Euclidean QCD vacuum. Since the vacuum state is gauge-invariant, only the gauge-invariant operators yield non-vanishing results once averaged over it. (This statement can be viewed as a corollary of the so-called Elitzur theorem [3,4], which states that a local gauge symmetry cannot be broken spontaneously.) For local composite operators, such asψψ or (F a µν ) 2 , gauge invariance holds automatically, and the mean values of these operators yield the QCD condensates [5,6]. Nevertheless, the quark and the gluon bound states are in general represented by the field operators which are defined at different points of the Euclidean space, so that a phase factor (also called a parallel transporter or a Schwinger string) interpolating between these points is required in order to provide gauge invariance of the full non-local operator. That is, the non-local gauge-invariant operators have, e.g., the formψ i (x)Φ ij xxwhere Φ ij xx and Φ ab xx are the phase factors transforming under the fundamental and the adjoint representations of SU(N), respectively, with i, j = 1, . . . , N and a, b = 1, . . . , N 2 − 1. (Throughout this review, we denote the number of colors by N.) Thus, the phase factors provide long-range correlations of color between individual quark...

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Field correlators in Abelian-projected theories and stochastic vacuum model

Cited by 30 publications

References 27 publications

k-string tensions in the 3-d SU(N) Georgi-Glashow model

k-string tensions in the 3-d SU(N) Georgi-Glashow model

3d Georgi–glashow Model and Confining Strings at Zero and Finite Temperatures

World-Line Formalism: Non-Perturbative Applications

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