Monopole Condensation In QCD Research Articles

Confinement of Fermions in Tachyon Matter

In this paper, we develop a phenomenological model inspired by QCD that mimics the QCD theory. We use the gauge theory in color dielectric medium (Gϕ) coupled with fermion fields to produce scalar and vector confinements in the chromoelectric flux tube scenario. The Abelian theory will be used to approximate the non-Abelian QCD theory in a consistent manner. We will calculate vector and scalar glueballs and compare the result to the existing simulation and experimental results and projections. The QCD-like vacuum associated with the model will be calculated and its behavior studied relative to changing quark masses. We will also comment on the relationship between tachyon condensation, dual Higgs mechanism, QCD monopole condensation, and their association with confinement. The behavior of the QCD string tension obtained from the vector potential of the model will be studied to establish vector dominance in confinement theories.

Abelian decomposition and Weyl symmetric effective action of SU(3) QCD

We show how to calculate the effective potential of SU(3) QCD which tells that the true minimum is given by the monopole condensation. To do this we make the gauge independent Weyl symmetric Abelian decomposition of the SU(3) QCD which decomposes the gluons to the color neutral neurons and the colored chromons. In the perturbative regime this decomposes the Feynman diagram in such a way that the conservation of color is explicit. Moreover, this shows the existence of two gluon jets, the neuron jet and chromon jet, which can be verified by experiment. In the non-perturbative regime, the decomposition puts QCD to the background field formalism and reduces the non-Abelian gauge symmetry to a discrete color reflection symmetry, and provides us an ideal platform to calculate the one-loop effective action of QCD. Integrating out the chromons from the Weyl symmetric Abelian decomposition of QCD gauge invariantly imposing the color reflection invariance, we obtain the SU(3) QCD effective potential which generates the stable monopole condensation and the mass gap. We discuss the physical implications of our result, in particular the possible existence of the vacuum fluctuation mode of the monopole condensation in QCD.

Abelian Decomposition and Monopole Condensation in QCD

We demonstrate the monopole condensation in QCD using the Abelian decomposition. The Abelian decomposition decomposes the gluons to the color neutral binding gluons (the neurons and the monopoles) and the colored valence gluons (the chromons), and shows that QCD can be viewed as the restricted QCD (RCD) made of the binding gluons which has the chromons as colored source. This simplifies the QCD dynamics greatly. In the perturbative regime this decomposes the gluon propagater to the neuron propagaters and the chromon propagaters, and simplifies the Feynman diagram. In the non-perturbative regime this allows us to calculate the QCD effective potential gauge independently, and demonstrate the monopole condensation unambiguously.

Dimensional Transmutation by Monopole Condensation in QCD

The dimensional transmutation by the monopole condensation in QCD is reviewed. Using Abelian projection of the gauge potential which projects out the monopole potential gauge independently, we we show that there are two types of gluons: the color neutral binding gluons which plays the role of the confining agent and the colored valence gluons which become confined prisoners. With this we calculate the one-loop QCD effective potential and show the monopole condensation becomes the true vacuum of QCD. We propose to test the existence of two types of gluons experimentally by re-analyzing the existing gluon jets data.

C-projection and monopole condensation in QCD

We show that the monopole condensation is responsible for the confinement. To demonstrate this we present a new gauge invariant integral expression of the one-loop QCD effective action which has no infra-red divergence, and show that the color reflection invariance ("the C-projection") assures the gauge invariance and the stability of the monopole condensation.

Dual Higgs Mechanism for Quarks in Hadrons

We study nonperturbative features of QCD using the dual Ginzburg-Landau (DGL) theory, where the color confinement is realized through the dual Higgs mechanism brought by QCD-monopole condensation. The linear confinement potential appears in the QCD-monopole condensed vacuum. We study the infrared screening effect to the confinement potential by the light-quark pair creation, and derive a compact formula for the screened quark potential. We study the dynamical chiral-symmetry breaking (DχSB) in the DGL theory by solving the Schwinger-Dyson equation. QCD-monopole condensation plays an essential role to DχSB. The QCD phase transition at finite temperature is studied using the effective potential formalism in the DGL theory. We find the reduction of QCD-monopole condensation and the string tension at high temperatures. The surface tension is calculated using the effective potential at the critical temperature Tc. The DGL theory predicts a large mass reduction of glueballs near Tc. We apply the DGL theory to the quark-gluon-plasma (QGP) physics in the ultrarelativistic heavy-ion collisions. We propose a new scenario of the QGP formation via the annihilation of color-electric flux tubes based on the attractive force between them.

Dimensional transmutation by monopole condensation in QCD

We compare two competing conjectures of the color confinement in QCD, the monopole condensation and the Abelian dominance, and show that it is the monopole condensation which is responsible for the confinement. To demonstrate this we present a new gauge invariant integral expression of the one-loop QCD effective action which has no infra-red divergence. With this we show that, just as the GSO-projection restores the supersymmetry and modular invariance in NSR string theory, the color reflection invariance ("the C-projection") assures the gauge invariance and the stability of the monopole condensation. This establishes the monopole dominance in QCD. In doing so we point out critical defects in the calculation of the Savvidy-Nielsen-Olesen (SNO) effective action.

QCD effective action and stability of magnetic condensation

We present two independent arguments to resolve the controversy on the stability of the magnetic condensation in QCD. We calculate the imaginary part of the one-loop effective action of SU(2) QCD in two different methods, and show that the gauge invariant calculation of the functional determinant assures the stability of the magnetic condensation. We confirm the stability calculating the imaginary part of the effective action perturbatively, with Fyenman diagram and Schwinger's method. We generalise this result to SU(3) QCD and show that, in the presence of chromomagnetic background, the real part of the effective action has true minimum only when H → 3 and H → 8 becomes orthogonal. Moreover, with the chromomagnetic background the effective action has no imaginary part, but with the chromoelectric background it acquires a negative imaginary part. This strongly indicates the existence of a stable monopole condensation in QCD.

CRITICAL PARAMETERS OF PHASE TRANSITION IN DUAL QCD

Color confinement is studied in dual version of SU (2) color gauge theory using its topological structure and the dynamical breaking of the magnetic symmetry which has been shown to effectively trigger the QCD monopole condensation in a dynamical way. The resulting flux tube structure of the QCD vacuum is explored which has been shown to lead to the perfect dual superconducting nature to the QCD vacuum in its dynamically broken phase. The analysis of the flux tube energy at different hadronic length scales has been shown to lead to the appearance of the strong confinement forces in QCD vacuum at large hadronic distances and an indication for the deconfinement phase at small scales. The analysis of the flux tube energy is then used to compute numerically the critical radius and the critical flux tube density of the phase transition from the flux tube phase to deconfined one inside hadrons. The numerical estimates are shown to be in fairly good agreement with the analytical values. The possible implications of these critical parameters on the formation of QGP as a result of the flux tubes fusion in intermediate energy regime are also discussed.

Chiral symmetry breaking and monopole condensation in QCD

We show that, in the dual superconductor picture of the QCD vacuum, the presence of the monopole condensate inevitably leads to the breaking of the chiral symmetry.

STABILITY OF MONOPOLE CONDENSATION IN SU(2) QCD

We propose to resolve the controversy regarding the stability of the monopole condensation in QCD by calculating the imaginary part of the one-loop effective action perturbatively. We calculate the imaginary part perturbatively to the order g2 with two different methods, with Feynman diagram and with Schwinger's method. Our result shows that with the magnetic background the effective action has no imaginary part, but with the electric background it acquires a negative imaginary part. This strongly indicates a stable monopole condensation in QCD.

A disorder analysis of the Ising model

Lattice studies of monopole condensation in QCD are based on the construction of a disorder parameter, a creation operator of monopoles which is written in terms of the gauge fields. This procedure is expected to work for any system which presents duality. We check it on the Ising model in 2 d, which is exactly solvable. The output is an amusing exercise in statistical mechanics.

Role of dual Higgs mechanism in chiral phase transition at finite temperature

The chiral phase transition at finite temperature is studied by using the Schwinger-Dyson equation in the dual Ginzburg-Landau theory, in which the dual Higgs mechanism plays an essential role on both the color confinement and the spontaneous chiral-symmetry breaking. At zero temperature, the quark condensate is strongly correlated with the string tension, which is generated by QCD-monopole condensation, as 〈 qq〉 1 3 ▪ σ . In order to solve the finite-temperature Schwinger-Dyson equation numerically, we provide a new ansatz for the quark self-energy in the imaginary-time formalism. The recovery of the chiral symmetry is found at high temperature; T C ∼ 100 MeV with realistic parameters. We find also a strong correlation between the critical temperature T C of the chiral symmetry restoration and the strength of the string tension.

Dual Ginzburg-Landau Theory with QCD-Monopoles for Dynamical Chiral-Symmetry Breaking

We study dynamical chiral-symmetry breaking of non-perturbative QCD in the dual Ginzburg-Landau theory, where the QCD-monopole field is introduced as an essential field for color confinement stemming from the choice of the abelian gauge fixing a la 't Hooft. In this theory, QCD-monopole condensation causes the dual Meissner effect, which changes the gluon propagator. The dynamical chiral-symmetry breaking is investigated using the Schwinger-Dyson equation with the modified gluon propagator in the QCD-monopole condensed vacuum. We introduce the low momentum cutoff on the modified gluon propagator by considering the effects of the pair creation and/or the quarks being confined in hadrons. We find that dynamical chiral-symmetry breaking is largely enhanced by QCD-monopole condensation, which suggests the close relation between the color confinement and the chiral symmetry breaking. The dynamical quark mass, the pion decay constant and the quark condensate are reproduced consistently with the confining mechanism in this theory.

Dual Higgs Mechanism for Quarks in Hadrons

We study nonperturbative features of QCD using the dual Ginzburg-Landau (DGL) theory, where the color confinement is realized through the dual Higgs mechanism brought by QCD-monopole condensation. The linear confinement potential appears in the QCD-monopole condensed vacuum. We study the infrared screening effect to the confinement potential by the light-quark pair creation, and derive a compact formula for the screened quark potential. We study the dynamical chiral-symmetry breaking (D$\chi $SB) in the DGL theory by solving the Schwinger-Dyson equation. QCD-monopole condensation plays an essential role to D$\chi $SB. The QCD phase transition at finite temperature is studied using the effective potential formalism in the DGL theory. We find the reduction of QCD-monopole condensation and the string tension at high temperatures. The surface tension is calculated using the effective potential at the critical temperature. The DGL theory predicts a large mass reduction of glueballs near the critical temperature. We apply the DGL theory to the quark-gluon-plasma (QGP) physics in the ultrarelativistic heavy-ion collisions. We propose a new scenario of the QGP formation via the annihilation of color-electric flux tubes based on the attractive force between them.

Magnetic monopole condensation for confinement and chiral symmetry breaking

Nonperturbative features of QCD are investigated using the dual Ginzburg-Landau theory. The quark confinement is realized through the dual Meissner effect, when QCD monopoles are condensed. The chiral symmetry is dynamically broken due to a large contribution of QCD-monopole condensation.