Abelian Confinement Mechanism and the QCD Vacuum

Maedan, Shinji; Matsubara, Yoshimi; Suzuki, Tsuneo

doi:10.1143/ptp.84.130

Cited by 114 publications

(215 citation statements)

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“…Attempts to accommodate a nonzero bare quark mass at least in an approximate way have been performed in Ref. [87] and recently in Ref. [88] where a generalized CDW ansatz was used in a variational approach.…”

Section: Eigenvalue Spectrum and Expectation Valuesmentioning

confidence: 99%

Inhomogeneous chiral condensates

Buballa

Carignano

2015

Progress in Particle and Nuclear Physics

241

258

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The chiral condensate, which is constant in vacuum, may become spatially modulated at moderately high densities where in the traditional picture of the QCD phase diagram a first-order chiral phase transition occurs. We review the current status of this idea, which originally dates back to Migdal's pion condensation, but recently received new momentum through studies on the nature of the chiral critical point and by the conjecture of a quarkyonic-matter phase. We discuss how these nonuniform phases emerge in generalized Ginzburg-Landau analyses as well as in specific calculations, both within effective models and in Dyson-Schwinger or large-N c approaches to QCD. Questions about the most favored shape of the modulations and its dimension, and about the effects of nonzero isospin chemical potential, strange quarks, color superconductivity, and external magnetic fields on these inhomogeneous phases will be addressed as well.

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Section: Eigenvalue Spectrum and Expectation Valuesmentioning

confidence: 99%

Inhomogeneous chiral condensates

Buballa

Carignano

2015

Progress in Particle and Nuclear Physics

241

258

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“…One can imagine these three fields as the dual red, dual blue and dual green EM fields. The second equation in (13) gives the same critical value for all components of the H (i) -fields:…”

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

confidence: 99%

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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“…Here, let us consider the application of this criterion to the effective theory of QCD in the abelian gauge, the dual Ginzburg-Landau (DGL) theory [28,29]. In the DGL theory, the local U(1) Nc−1 and the global Weyl symmetries remain, and the dual gauge field B µ and the monopole field χ α [α=1, · · ·, 1 2 N c (N c − 1)] are the relevant modes for infrared physics.…”

Section: Residual Symmetry and Gauge Invariance Condition In The mentioning

confidence: 99%

“…Ezawa and Iwazaki formulated the dual London theory as an infrared effective theory of QCD, and later it is reformulated as the dual Ginzburg-Landau theory [28][29][30][31][32][33][34].…”

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confidence: 99%

Abelian dominance for confinement and random phase property of off-diagonal gluons in the maximally abelian gauge

Ichie

Suganuma

1999

Nuclear Physics B

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We study abelian dominance for confinement in terms of the local gluon properties in the maximally abelian (MA) gauge in a semi-analytical manner with the help of the lattice QCD. The global Weyl symmetry persistently remains as the relic of SU(N c ) in the MA gauge, and provides the ambiguity on the electric and magnetic charges. We derive the criterion on the SU(N c )-gauge invariance in terms of the residual symmetry in the abelian gauge. In the lattice QCD, we find microscopic abelian dominance on the link variable for the whole region of β in the MA gauge. The off-diagonal angle variable, which is not constrained by the MA-gauge fixing condition, tends to be random besides the residual gauge degrees of freedom. Within the randomvariable approximation for the off-diagonal angle variable, we prove that off-diagonal gluon contribution to the Wilson loop obeys the perimeter law in the MA gauge, and show exact abelian dominance for the string tension, although small deviation is brought by the finite size effect of the Wilson loop in the actual lattice QCD simulation. *

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Abelian Confinement Mechanism and the QCD Vacuum

Cited by 114 publications

References 0 publications

Inhomogeneous chiral condensates

Inhomogeneous chiral condensates

Gluodynamics in external field in dual superconductor approach

Abelian dominance for confinement and random phase property of off-diagonal gluons in the maximally abelian gauge

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