Casimir scaling in a dual superconducting scenario of confinement

Koma, Yoshiaki; Ilgenfritz, E. M.; Toki, H.; Suzuki, Tsuneo

doi:10.1103/physrevd.64.011501

Cited by 49 publications

(87 citation statements)

References 20 publications

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“…The critical values are equivalent due to the Weyl symmetry of the dual model [17,18] which states that the [U(1)] 2 Lagrangian (10) is invariant under the transformations of the dual gauge fields B 3,8 corresponding to the mutual permutations of the H (i) fields (14). The string tension spanned between the fundamental charges (quarks) in the Bogomol'ny limit (12) of the SU(3) gluodynamics is [16,17] σ = 2πη 2 .…”

Section: Now Let Us Consider the Lagrangian Of [U(1)] 2 Higgs Model Cmentioning

confidence: 99%

“…Thus in the A 12 phase we expect the existence of the relatively heavy meson composed from red quarks and two lighter mesons made of blue and green quarks 4 . The observed color asymmetry in the meson states is caused by the breaking of the Weyl symmetry [17,18] of the Lagrangian (10) by the external field.…”

mentioning

confidence: 99%

“…In the confinement phase all three monopole fields, Φ i , i = 1, 2, 3, are condensed and the [U(1)] 2 model possesses three types of vortex solutions [15,18,20] which confine all quarks into bound states. Each vortex solution is characterized by the winding number n i , Φ i ∝ e in i φ i , where φ i is the azimuth angle.…”

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Gluodynamics in external field in dual superconductor approach

Chernodub

2002

Physics Letters B

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We show that gluodynamics in an external Abelian electromagnetic field should possess a deconfining phase transition at zero temperature. Our analytical estimation of the critical external field is based on the dual superconductor picture which is formulated in the Euclidean space suitable for lattice calculations. A dual superconductor model corresponding to the SU (2) gluodynamics possesses confinement and deconfinement phases below and, respectively, above the critical field. A dual superconductor model for the SU (3) gauge theory predicts a rich phase structure containing confinement, asymmetric confinement and deconfinement phases. The quark bound states in these phases are analyzed. Inside the baryon the strings are Y -shaped as predicted by the dual superconductor picture. This shape is geometrically asymmetric in the asymmetric confinement phases.1. At present there are two popular approaches to the problem of color confinement in gluodynamics. They are based on the Abelian monopole [1] and on the center vortex [2] pictures of the gluodynamics vacuum. In this paper we discuss the Abelian monopole approach which suggests that confining degrees of freedom of the vacuum in an Abelian projection [3] can be described as a dual superconductor. The key element of this picture is the monopole condensate which squeezes a chromoelectric flux to a confining string due to the Meissner effect. The string is an analog of the Abrikosov vortex [4] in an ordinary superconductor while the Abelian monopoles are playing the role of the Cooper pairs. This picture has been confirmed in many numerical simulations on the lattice (for a review see, e.g., Ref. [5]).Here we investigate the properties of the SU(2) and SU(3) gluodynamics in the external electromagnetic field using the dual superconductor approach. Our study is motivated by the fact that the response of the vacuum of a gauge theory on external fields may provide interesting information about the vacuum structure. The external fields were used to study nonperturbative properties of QCD [6], the baryogenesis in the electroweak theory [7], features of various topological defects in three dimensional models [8], etc.A common feature of known superconductors is the Meissner effect: the superconductors expel relatively weak external magnetic flux from their interior. Strong enough magnetic field, H ext H cr destroys the superconductivity and the superconductor goes in the normal (metal) state. In this paper we estimate analytically the critical electromagnetic fields which break the dual superconductivity in the SU(2) and SU(3) gluodynamics. Consequently, the confinement is (partially, in the case of SU(3)) lost at these critical fields.

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Section: Now Let Us Consider the Lagrangian Of [U(1)] 2 Higgs Model Cmentioning

confidence: 99%

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Gluodynamics in external field in dual superconductor approach

Chernodub

2002

Physics Letters B

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“…In the DGL theory, the quark confinement mechanism is described by the formation of a color-electric flux-tube due to a dual Meissner effect. The ratios between string tensions of charges in higher and fundamental SU (3) DGL theory cast into a Weyl symmetric formulation [12,13]. It has been shown that the ratios depend on the GL parameter, κ ≡ m χ /m B .…”

Section: Introductionmentioning

confidence: 99%

“…[8], one of the present authors has examined the dual Ginzburg-Landau (DGL) theory [9,10,11] as a QCD-vacuum model under this aspect. In the DGL theory, the quark confinement mechanism is described by the formation of a color-electric flux-tube due to a dual Meissner effect.…”

Section: Introductionmentioning

confidence: 99%

Systematics of flux tubes in the dual Ginzburg-Landau theory and Casimir scaling hypothesis: folklore and lattice facts

Koma

2003

Eur. Phys. J. C

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Abstract. The ratios between string tensions σD of color-electric flux tubes in higher and fundamental SU(3) representations, dD ≡ σD/σ3, are systematically studied in a Weyl symmetric formulation of the DGL theory. The ratio is found to depend on the Ginzburg-Landau (GL) parameter, κ ≡ mχ/mB, the mass ratio between monopoles (mχ) and dual gauge bosons (mB). While the ratios dD follow a simple flux counting rule in the Bogomol'nyi limit, κ = 1.0, systematic deviations appear with increasing κ due to interactions between fundamental flux inside a higher representation flux tube. We find that in a type-II dual superconducting vacuum near κ = 3.0 this leads to a consistent description of the ratios dD observed in lattice QCD simulations.

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Flux tubes at finite temperature

Cea

Cosmai

Cuteri

et al. 2016

J. High Energ. Phys.

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The chromoelectric field generated by a static quark-antiquark pair, with its peculiar tube-like shape, can be nicely described, at zero temperature, within the dual superconductor scenario for the QCD confining vacuum. In this work we investigate, by lattice Monte Carlo simulations of the SU(3) pure gauge theory, the fate of chromoelectric flux tubes across the deconfinement transition. We find that, if the distance between the static sources is kept fixed at about 0.76 fm 1.6/ √ σ and the temperature is increased towards and above the deconfinement temperature T c , the amplitude of the field inside the flux tube gets smaller, while the shape of the flux tube does not vary appreciably across deconfinement. This scenario with flux-tube "evaporation" above T c has no correspondence in ordinary (type-II) superconductivity, where instead the transition to the phase with normal conductivity is characterized by a divergent fattening of flux tubes as the transition temperature is approached from below. We present also some evidence about the existence of flux-tube structures in the magnetic sector of the theory in the deconfined phase.

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Casimir scaling in a dual superconducting scenario of confinement

Cited by 49 publications

References 20 publications

Gluodynamics in external field in dual superconductor approach

Gluodynamics in external field in dual superconductor approach

Systematics of flux tubes in the dual Ginzburg-Landau theory and Casimir scaling hypothesis: folklore and lattice facts

Flux tubes at finite temperature

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