String representation of field correlators in the Dual Abelian Higgs Model

Antonov, Dmitri; Эберт, Д.

doi:10.1007/s100520050468

Cited by 16 publications

(30 citation statements)

References 28 publications

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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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Section: Correlation Lengths Of the Stochastic Yang-mills Fieldsmentioning

confidence: 99%

World-Line Formalism: Non-Perturbative Applications

Bellettre

2016

Universe

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“…[20] in 4-d and in ref. [21] in 3-d), in particular with the applications to the stochastic vacuum model [22,23]; the jacobian of the transformation from field to string variables has been discussed in ref. [24]; the SU(N ) generalization has been explored, in particular for studies of the θ-term [25] [see ref.…”

Section: Jhep12(2004)022mentioning

confidence: 99%

k-string tensions in the 4-d SU(N)-inspired dual Abelian-Higgs-type theory

Antonov¹,

Debbio²,

Эберт³

2004

J. High Energy Phys.

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The k-string tensions are explored in the 4-d [U(1)] N −1 -invariant dual abelianHiggs-type theory. In the London limit of this theory, the Casimir scaling is found in the approximation when small-sized closed dual strings are disregarded. When these strings are treated in the dilute-plasma approximation, explicit corrections to the Casimir scaling are found. The leading correction due to the deviation from the London limit is also derived. Its N -ality dependence turns out to be the same as that of the first non-trivial correction produced by closed strings. It also turns out that this N -ality dependence coincides with that of the leading correction to the k-string tension, which emerges by way of the nondiluteness of the monopole plasma in the 3-d SU(N ) Georgi-Glashow model. Finally, we prove that, in the latter model, Casimir scaling holds even at monopole densities close to the mean one, provided the string world sheet is flat.

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“…(40) can be written as We now take J µν to be the vorticity tensor current [4][5][6][7] J µν Σ (x) ≡ 2πQ…”

Section: Noncovariant Quantization In Axial Gaugementioning

confidence: 99%

“…Recently, an extended dual Abelian Higgs model (EDAHM) has been proposed by Baker et al [3] and by Antonov and Ebert [4] to incorporate external (color-)electric charges such as quarks into the DAHM. Using the path integral method [5,6], Antonov and Ebert have also derived a dual form of the Lagrangian that defines the EDAHM in the London limit.…”

Section: Introductionmentioning

confidence: 99%