Phase transition over the gauge group center and quark confinement in QCD

Khokhlachev, S.B.; Makeenko, Yuri

doi:10.1016/0370-2693(81)90163-5

Cited by 24 publications

(10 citation statements)

References 7 publications

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“…We see that the ratio of the leading contributions to Equation (14), which stems from the 1 z -parts of the integrals J 2 and I 2 at sufficiently small z, remains the same as at zero temperature. Consequently, the above-obtained zero-temperature results (19) and (20) remain valid up to temperatures at which the theory undergoes the dimensional reduction, becoming effectively three-dimensional.…”

Section: Calculationmentioning

confidence: 70%

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Paramagnetic versus Diamagnetic Interaction in the SU(2) Higgs Model

Bellettre¹

2019

Symmetry

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We present an analytic calculation of the paramagnetic and diamagnetic contributions to the one-loop effective action in the SU(2) Higgs model. The paramagnetic contribution is produced by the gauge boson, while the diamagnetic contribution is produced by the gauge boson and the ghost. In the limit, where these particles are massless, the standard result of - 12 for the ratio of the paramagnetic to the diamagnetic contribution is reproduced. If the mass of the gauge boson and the ghost become much larger than the inverse vacuum correlation lengths of the Yang–Mills vacuum, the value of the ratio goes to - 8 . We also find that the same values of the ratio are achieved in the deconfinement phase of the model, up to the temperatures at which the dimensional reduction occurs.

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Section: Calculationmentioning

confidence: 70%

“…This leads to the appearance of two 1-gluon gluelumps and yields the perimeter-law exponential in the Wilson loop of the heavy adjoint source. This exponential has the form e −ML , where L is the length of the contour C. The full adjoint Wilson loop reads [19][20][21][22]…”

Section: The Modelmentioning

confidence: 99%

Paramagnetic versus Diamagnetic Interaction in the SU(2) Higgs Model

Bellettre¹

2019

Symmetry

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“…The adjoint string interconnecting the gluon with the static source, breaks upon the creation of a glueball and the subsequent recombination process. This leads to the formation of two one-gluon gluelumps, which correspond to the perimeter-law exponential e −ML in the adjoint Wilson loop, where L is the length of the contour C. Accordingly, in the limit of large number of colors N, the adjoint Wilson loop is assumed to be of the form [66][67][68][69] …”

Section: Electroweak Phase Transition As a Vacuum Instabilitymentioning

confidence: 99%

“…Upon this factorization, the world-line integral over z 4 (τ) in Equation (66) becomes that of a free particle, which yields…”

Section: Free Energy Of the Gluon Plasma In The High-temperature Limitmentioning

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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“…This issue was analyzed a long time ago [7,8], and it was noted, that unbroken symmetry locally confines quarks so that they cannot move separately even at the lattice scales. It was suggested in the recent work [6], that this symmetry breaks spontaneously at the transition point, as it does in the mean field approximation [7,8]. In any case, this is the problem for the higher 1 N approximations, as the center of the gauge group is negligible at N = ∞.…”

Section: Introductionmentioning

confidence: 99%

1/N Expansion and Particle Spectrum in Induced QCD

Migdal

1993

Mod. Phys. Lett. A

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We study the 1 N expansion in the recently proposed model of the lattice gauge theory induced by heavy scalar field in adjoint representation. In the first approximation the fluctuations of the density of eigenvalues of the scalar field are Gaussian, so that the scalar glueball spectrum is defined from the corresponding linear wave equation. 0The problem of solving large N QCD seemed hopeless until recently some new approach was taken [2,3]. Instead of trying to solve it starting from the asymptotic freedom, we suggested to start much earlier, at such scales, that there are no gluons yet, but rather some gluon constituents.The idea is that one could then use the freedom of choosing any constituents and any form of their interaction, as long as the effective theory at large scales would be still QCD. Clearly the gauge symmetry should be there from the start, but there need not be the Yang-Mills (or Wilson, in the lattice formulation) term in the bare Action. This term should be induced in an asymptotically free region, as result of integrating out heavy constituents.This idea is quite old. Perhaps Sakharov was the first one to suggest the induced Gravity. After that the idea was unsuccessfully implemented by the author (see the review paper[1]) in the fermionic string model of QCD. The heavy constituents were introduced as 2-dimensional Majorana fermions at the world sheet of string. Formally, the Schwinger-Dyson equations of the large N QCD were satisfied, but one could not make any sense out of this model.As we see it now, after ten more years of study of the string theory, the real problem comes from the string. Apparently, there is no such thing as a noncritical string in any number D > 1 of external dimensions. The interaction at the world sheet must be essentially nonlocal, and/or it should involve some extrinsic geometry. The idea of string realization of the Lorentz group was a beautiful one, and it still has chance to work in Gravity, but in QCD I personally do not believe in this idea any more. Apparently, the coordinates could only be arguments of fields, rather then fields in QCD.Coming back to the induced QCD, the idea of Kazakov and myself was to take heavy scalar field in adjoint representation of the gauge group as a constituent field. Naively, if one just integrates this field out, one induces the correct Yang-Mills action, with positive coefficient in front, scaling correctly at large N. By the way, the simpler choice of the fundamental representation would yield too large induced gauge coupling, so it could not induce an asymptotically free QCD at large N. The large (∼ N) number of fundamental scalars would do it, but this model is hard to solve.The correct computation of induced gauge coupling is not so trivial, as there are feedback effects from induced hard gluons, and those from effective scalar quartic interaction. If one starts from asymptotically free region, and goes to smaller scales, there would be two conflicting effects. First, there would be antiscreening of gauge coupling from the ...

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Phase transition over the gauge group center and quark confinement in QCD

Cited by 24 publications

References 7 publications

Paramagnetic versus Diamagnetic Interaction in the SU(2) Higgs Model

Paramagnetic versus Diamagnetic Interaction in the SU(2) Higgs Model

World-Line Formalism: Non-Perturbative Applications

1/N Expansion and Particle Spectrum in Induced QCD

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