Faddeev–Niemi conjecture and effective action of QCD

Cho, Y.M.; Lee, H.W.; Pak, D. G.

doi:10.1016/s0370-2693(01)01450-2

Cited by 51 publications

(121 citation statements)

References 40 publications

(40 reference statements)

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“…A satisfactory theoretical proof of the desired monopole condensation in QCD, however, has been very elusive [4,5,6]. Fortunately, we have recently been able to demonstrate the monopole condensation with the one-loop effective action in SU (2) QCD [7,8]. In this paper we discuss the perturbative method which can prove the stability of the monopole condensation in detail.…”

Section: Introductionmentioning

confidence: 96%

“…A few years ago, however, there was a new attempt to calculate the one-loop effective action of QCD with a gauge independent separation of the classical background from the quantum field [7]. Remarkably, in this calculation the effective action was shown to produce no imaginary part in the presence of the non-Abelian monopole background, but a negative imaginary part in the presence of the pure color electric background.…”

Section: Introductionmentioning

confidence: 99%

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Monopole Condensation and Dimensional Transmutation in SU(2) QCD

Cho

Walker

Pak

2004

J. High Energy Phys.

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We resolve the controversy on the stability of the monopole condensation in the one-loop effective action of SU (2) QCD by calculating the imaginary part of the effective action with two different methods at one-loop order. Our result confirms that the effective action for the magnetic background has no imaginary part but the one for the electric background has a negative imaginary part. This assures that the monopole condensation is indeed stable, but the electric background becomes unstable due to the pair-annihilation of gluons.

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Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Monopole Condensation and Dimensional Transmutation in SU(2) QCD

Cho

Walker

Pak

2004

J. High Energy Phys.

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“…The first two terms in (1) coincide with respective first two terms in the original Skyrme Lagrangian after proper changing variable for the scalar field. The last term in the Lagrangian appears in the one-loop effective action of standard QCD as it was shown in [14,16]. The topological content of the theory is determined by the CP 1 fieldn realizing the Hopf mapping.…”

mentioning

confidence: 91%

“…It is proposed to interpret such knot solutions as color electric and color magnetic glueball states [8,[10][11][12][13]. One should notice, that derivation of a strict expression for a low energy effective action from the basics of QCD is an extremely difficult problem [14][15][16]. So far there exists a number of various extended Skyrme-Faddeev models where some exact and numeric knot and vortex solutions have been found [17][18][19][20].…”

mentioning

confidence: 99%

“…In general the low energy effective action of QCD contains scalar fields [10] which originate from unknown coefficient correlation functions in the effective action and play roles of order parameters in the effective theory [14]. We consider a minimal extension of the Skyrme-Faddeev theory to find out a model which is similar to the Skyrme theory, and, at the same time, inherits properties of integrable CP 1 models.…”

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confidence: 99%

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Exact knot solutions in a generalized Skyrme-Faddeev model

2013

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We propose a generalized Skyrme-Faddeev type theory with an additional scalar field. In a special case of model parameters one has a theory which admits exact knot solutions given by a class of exact toroidal solitons from Aratyn-Ferreira-Zimerman (AFZ) integrable CP 1 model. In a general case the theory admits an exact knot solution for a unit Hopf charge. For higher Hopf charges we perform numeric analysis of the solutions and obtain estimates for the knot energies using energy minimization procedure based on ansatz with AFZ field configurations and with rational functions. We show that AFZ configurations provide a better approximate solutions. The corresponding knot energies are in a good agreement with a standard law for the low energy bound, EH Q [6,7]. The Skyrme-Faddeev theory [8,9] represents another kind of effective theories which supposed to be induced from quantum chromodynamics (QCD) in low energy regime. The theory possesses topological knot solitons classified by the homotopy group π 3 (CP 1 ) = Z, i.e., by the topological Hopf charge. It is proposed to interpret such knot solutions as color electric and color magnetic glueball states [8,[10][11][12][13]. One should notice, that derivation of a strict expression for a low energy effective action from the basics of QCD is an extremely difficult problem [14][15][16]. So far there exists a number of various extended Skyrme-Faddeev models where some exact and numeric knot and vortex solutions have been found [17][18][19][20].In the present paper we consider an extended SkyrmeFaddeev model with an additional scalar field. In general the low energy effective action of QCD contains scalar fields [10] which originate from unknown coefficient correlation functions in the effective action and play roles of order parameters in the effective theory [14]. We consider a minimal extension of the Skyrme-Faddeev theory to find out a model which is similar to the Skyrme theory, and, at the same time, inherits properties of integrable CP 1 models.So far, all known topological solutions in (3+1) Skyrme type models are obtained numerically except the original Skyrmion soliton [1]. Some exact vortex solutions have been obtained in a generalized Skyrme-Faddeev theory for a special set of model parameters which imply the existence of integrable submodel in the theory [17][18][19]. A family of exact analytic knot solutions with toroidal configuration have been constructed in special integrable CP 1 models [21,22]. Unfortunately, physical applications of such solutions in QCD remain unclear. We propose a Skyrme-Faddeev-type model which admits exact knot solutions and which can give some hints towards constructing a more realistic low energy QCD effective theory. Let us consider an extended Skyrme-Faddeev model defined by the following Lagrangianwheren is a unit triplet field in adjoint representation of SU (2) color group, i.e., CP 1 field, φ is a real scalar field, and H µν is a magnetic field defined as followsµ, β, ν, ξ are model parameters. The first two terms in (1) ...

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Quantization of the Restricted Gauge Theory of QCD 2

Kulshreshtha

2015

Few-Body Syst

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In this talk, we consider the restricted gauge theory of QCD 2à la Cho et al. and study its quantization using Hamiltonian, path integral and BRST quantization procedures.In this talk, we consider the restricted gauge theory of QCD 2 [1-27]à la Cho et al. and study its quantization using Hamiltonian [28], path integral [29][30][31][32] and BRST [29] quantization procedures, in the usual instant-form (IF) of dynamics (on the hyperplanes: x 0 = t = constant) [33,34]. We first briefly recap the basics of the so-called restricted gauge theory of QCD 2 due to Cho et al. . The theory makes use of the so-called "Cho-decomposition", which is, in fact, the gauge independent decomposition of the non-Abelian potential into the restricted potential and the valence potential and it helps in the clarification of the topological structure of the non-Abelian gauge theory, and it also takes care of the topological characters in the dynamics. The non-Abelian gauge theory has rich topological structures manifested by the non-Abelian monopoles, the multiple vacuua and the instantons and one needs to take into account these topological characters in the nonAbelian dynamics. Since the decomposition of the non-Abelian connection contains these topological degrees explicitly, it can naturally take care of them in the non-Abelian dynamics. An important consequence of the decomposition is that it allows one to view QCD as the restricted gauge theory (made of the restricted potential) which is coupled to a gauge-covariant colored vector field (the valence potential). The restricted potential is defined in such a way that it allows a covariantly constant unit isovectorn everywhere in space-time, which enables one to define the gauge-independent color direction everywhere in space-time and at the same time allows one to define the magnetic potential of the non-Abelian monopoles. Furthermore it has the full SU(2) gauge degrees of freedom, in spite of the fact that it is restricted. Consequently, the restricted QCD made of the restricted potential describes a very interesting dual dynamics of its own, and plays a crucial role in the understanding of QCD. On the other hand, the restricted QCD is a constrained system, due to the presence of the topological fieldn which is constrained to have the unit norm. A natural way to accommodate the topological degrees into the theory is to introduce a topological fieldn of unit norm, and to decompose the connection into the Abelian projection part which leavesn a covariant constant and the remaining part which forms a covariant vector field: A μ = (A μn − 1 gn × ∂ μn + X μ ) = (Â μ + X μ ); A μ =n · A μ andn 2 = 1. Here A μ is the "electric" potential and the Abelian projection A μ is precisely the connection which leavesn invariant under the parallel transport and makesn a covariant constant:D μn = (∂ μn + gÂ μ ×n) = 0 Also, under the infinitesimal gauge transformation: δn = − α ×n, δA μ = 1 g D μ α, δ A μ = 1 gn · ∂ μ α, δÂ μ = 1 gD μ α, δX μ = − α × X μ (1)

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Faddeev–Niemi conjecture and effective action of QCD

Cited by 51 publications

References 40 publications

Monopole Condensation and Dimensional Transmutation in SU(2) QCD

Monopole Condensation and Dimensional Transmutation in SU(2) QCD

Exact knot solutions in a generalized Skyrme-Faddeev model

Quantization of the Restricted Gauge Theory of QCD 2

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