In a functional approach to QCD the infrared behaviour of Landau gauge Green functions is investigated. Positivity violation for, and thus confinement of, gluons is demonstrated, and the analytic structure of the gluon propagator is studied. Quark confinement is related to an infrared divergence of the quark-gluon vertex. In the latter various components are dynamically induced due to the spontaneous breaking of chiral symmetry. As a result an infrared finite running coupling in the Yang-Mills sector is derived whereas the running coupling related to the quark-gluon vertex is infrared divergent. Based on a truncation for the quark-gluon vertex Dyson-Schwinger equation, which respects the analytically determined infrared behavior, numerical results for the coupled system of the quark propagator and vertex Dyson-Schwinger equations are presented. The resulting quark mass function as well as the vertex function show only a very weak dependence on the current quark mass in the deep infrared. From this we infer by an analysis of the quark-quark scattering kernel a linearly rising quark potential with an almost mass independent string tension in the case of broken chiral symmetry.
An introduction is given into current lattice investigations of the non-perturbative gluon and ghost propagators, in the light of the Gribov-Zwanziger and Kugo-Ojima scenarios of confinement, in the context of results obtained from the non-perturbative Dyson-Schwinger approach in the continuum and in connection with the vortex mechanism of confinement.
We study nonperturbative features of QCD using the dual Ginzburg-Landau theory. The color confinement is realized through the dual Higgs mechanism, which is brought by QCD-monopole condensation. We investigate the infrared screening effect on the color confinement due to the light-quark pair creation. By solving the Schwinger-Dyson equation, we find that the dynamical chiral-symmetry breaking is largely brought by the confining force.
Nonperturbative features of QCD are studied using the dual Ginzburg-Landau (DGL) theory with QCD-monopoles. The linear quark potential appears in the QCD-monopole condensed vacuum. We find that QCD-monopole condensation plays an essential role to the dynamical chiral-symmetry breaking. We also investigate the QCD phase transition at finite temperature in the DGL theory.
We review aspects of confinement in the covariant and local description of QCD and discuss to what extend our present knowledge of the infrared behavior of QCD Green functions can support this description. In particular, we emphasize: the positivity violations of transverse gluon and quark states, the Kugo-Ojima confinement criterion, and the conditions necessary to avoid the decomposition property for colored clusters. We summarize how these issues relate to the infrared behavior of the propagators in Landau gauge QCD as extracted from solutions to truncated Dyson-Schwinger equations and latt…
Using the effective potential formalism, we study dynamical chiral symmetry breaking (D$χ$SB) in the dual Ginzburg-Landau (DGL) theory, where the color confinement is brought by monopole condensation. The effective potential as a function of infrared quark mass is found to have double-well structure, which leads to spontaneous breaking of chiral symmetry. To examine the role of confinement, we divide the effective potential into the confinement part and others, which correspond to the confinement term and other (Yukawa, Coulomb) terms of the gluon propagator in the DGL theory. It is found that…
The infrared behaviour of the gluon and ghost propagators in Landau gauge QCD is reviewed. The Kugo-Ojima confinement criterion and the Gribov-Zwanziger horizon condition result from quite general properties of the ghost Dyson-Schwinger equation. The numerical solutions for the gluon and ghost propagators obtained from a truncated set of Dyson-Schwinger equations provide an explicit example for the anticipated infrared behaviour. The results are in good agreement with corresponding lattice data obtained recently. The resulting running coupling approaches a fix point in the infrared, $α(0) = 8.…
The Kugo-Ojima confinement criterion and its relation to the infrared behaviour of the gluon and ghost propagators in Landau gauge QCD are reviewed. The realization of this confinement criterion (which in Landau gauge relates to Zwanziger's horizon condition) results from quite general properties of the ghost Dyson-Schwinger equation. The numerical solutions for the gluon and ghost propagators obtained from a truncated set of Dyson-Schwinger equations provide an explicit example for the anticipated infrared behaviour. These results are in good agreement, also quantitatively, with corresponding…
The infrared behaviour of Landau gauge QCD vertex functions is investigated employing a skeleton expansion of the Dyson-Schwinger and Renormalization Group equations. Results for the ghost-gluon, three-gluon, four-gluon and quark-gluon vertex functions are presented. Positivity violation of the gluon propagator, and thus gluon confinement, is demonstrated. Results of the Dyson-Schwinger equations for a finite volume are compared to corresponding lattice data. It is analytically demonstrated that a linear rising potential between heavy quarks can be generated by infrared singularities in the dr…
We summarise an analysis of the infrared regime of Landau gauge QCD by means of a flow equation approach. The infrared behaviour of gluon and ghost propagators is evaluated. The results provide further evidence for the Kugo-Ojima confinement scenario. We also discuss their relation to results obtained with other functional methods as well as the lattice.
Recent investigations of the Dyson-Schwinger equations and Monte-Carlo lattice calculations resulted in a coherent description of the fully dressed gluon, ghost and quark propagators in Landau gauge QCD. In the Dyson-Schwinger approach the infrared behaviour of these propagators is determined analytically. For finite spacelike momenta the gluon, ghost and quark propagators are compared to available corresponding results of lattice Monte-Carlo calculations. For all three propagators an almost quantitative agreement is found. These results for the non-perturbative propagators allow an analytical…
I give a brief account of Gribov's scenario of supercritical charges in QCD. Gribov's equation for the Green function of light quarks and its derivation from the corresponding Dyson-Schwinger equation are described. The resulting Green function is shown to exhibit chiral symmetry breaking.
We study the color confinement, the $q$-$\bar q$ pair creation and the dynamical chiral-symmetry breaking of nonperturbative QCD by using the dual Ginzburg-Landau theory, where QCD-monopole condensation plays an essential role on the nonperturbative dynamics in the infrared region. As a result of the dual Meissner effect, the linear static quark potential, which characterizes the quark confinement, is obtained in the long distance within the quenched approximation. We obtain a simple expression for the string tension similar to the energy per unit length of a vortex in the superconductivity ph…
We analyse the complete algebraic structure of the background field method for Yang--Mills theory in the Landau gauge and show several structural simplifications within this approach. In particular we present a new way to study the IR behavior of Green functions in the Landau gauge and show that there exists a unique Green function whose IR behaviour controls the IR properties of the gluon and the ghost propagators.
I analyze the IR fixed point structure of Landau gauge QCD. Precisely the fixed point with a strong kinematic singularity of the quark-gluon vertex that proved crucial for the recently proposed confinement mechanism in the quenched approximation is absent in dynamical QCD. Therefore, the IR singularities do not induce asymptotic quark confinement but the long-range interaction is screened by unquenching loops at scales of the order of the quark mass. This provides the prerequisite for a microscopic description of deconfinement and string breaking. The fixed points determine the qualitative for…
Prerequisites of confinement in the covariant and local description of QCD are reviewed. In particular, the Kugo-Ojima confinement criterion, the positivity violations of transverse gluon and quark states, and the conditions necessary to avoid the decomposition property for colored clusters are discussed. In Landau gauge QCD, the Kugo-Ojima confinement criterion follows from the ghost Dyson-Schwinger equation if the corresponding Green's functions can be expanded in an asymptotic series. Furthermore, the infrared behaviour of the propagators in Landau gauge QCD as extracted from solutions to t…
Expanding the Landau gauge gluon and ghost two-point functions in a power series we investigate their infrared behavior. The corresponding powers are constrained through the ghost Dyson-Schwinger equation by exploiting multiplicative renormalizability. Without recourse to any specific truncation we demonstrate that the infrared powers of the gluon and ghost propagators are uniquely related to each other. Constraints for these powers are derived, and the resulting infrared enhancement of the ghost propagator signals that the Kugo-Ojima confinement criterion is fulfilled in Landau gauge Yang-Mil…
Simulations of SU(2) lattice gauge theory are used to establish a relation between the IR properties of Green functions and confinement. Using Landau gauge where the gauge configurations are restricted to the first Gribov regime, results on the ghost-, gluon form-factor and the running coupling constant are presented. Finally, we discuss the behavior of the ghost form-factor of the de-confined phase at high temperatures.
The vortex picture of confinement is employed to explore the signals of confinement in Yang-Mills Green functions. By using SU(2) lattice gauge theory, it has been well established that the removal of the center vortices from the lattice configurations results in the loss of confinement. The running coupling constant, the gluon and the ghost form factors are studied in Landau gauge for both cases, the full and the vortex removed theory. In the latter case, a strong suppression of the running coupling constant and the gluon form factor at low momenta is observed. At the same time, the singulari…
Confinement and chiral symmetry breaking are the most fundamental phenomena in Quark Nuclear Physics, where hadrons and nuclei are described in terms of quarks and gluons. The dual Ginzburg-Landau (DGL) theory, which contains monopole fields as the most essential degrees of freedom and their condensation in the vacuum, is modeled to describe quark confinement in strong connection with QCD. We then demonstrate that the DGL theory is able to describe the spontaneous break down of the chiral symmetry.
A brief and biased overview of the phenomenon of confinement in QCD is presented in three parts: (1) the definition of confinement, (2) properties of confinement, (3) ideas of confinement. The second part chiefly consists of a brief review of recent lattice computations related to confinement while the third summarizes some of the current analytical approaches to understanding confinement. These include the Dyson-Schwinger formalism in Landau gauge, Hamiltonian QCD in Coulomb gauge, and the vortex picture of confinement.
I give a brief description of Gribov's light quark confinement scenario and of the Gribov--Dyson--Schwinger equation for light quarks. It is shown that the Green function obtained from this equation exhibits chiral symmetry breaking.
After presenting a brief summary of functional approaches to QCD at vanishing temperatures and densities the application of QCD Green's functions at non-vanishing temperature and vanishing density is discussed. It is pointed out in which way the infrared behavior of the gluon propagator reflects the (de-)confinement transition. Numerical results for the quark propagator are given thereby verifying the relation between (de-)confinement and dynamical chiral symmetry breaking (restoration). Last but not least some results of Dyson-Schwinger equations for the color-superconducting phase at large d…
The infrared behaviour of the standard model at finite temperature is determined by the confining phase of the SU(2)-Higgs model in three dimensions. Due to the Landau singularity of the three-dimensional gauge theory the perturbative treatment of the electroweak phase transition breaks down for Higgs masses above a critical mass $m_H^c$. Based on a renormalization group improved effective potential we find $m_H^c\sim$ 70 GeV. The scalar self-coupling has a Landau-type singularity also in the abelian U(1)-Higgs model, which leads to a breakdown of perturbation theory in the symmetric phase.
In light of the development of the Gribov issue for pure Euclidean gauge theories and of the recent lattice measurement of soft breaking of the BRST invariance in Yang-Mills theories in the Landau gauge, we consider non-perturbative features in the gauge-interacting matter sector and their relation with general properties of the Faddeev-Popov operator. A signature for BRST breaking in the matter sector is proposed and a local and renormalizable framework is constructed, accommodating this signature and predicting non-perturbative matter propagators that are consistent with available lattice da…
On the lattice we study the gauge boson propagator of three dimensional compact QED in Landau gauge at zero and non-zero temperature. The non-perturbative effects are taken into account by the generation of a mass, by an anomalous dimension and by the photon wave function renormalization. All these effects can be attributed to the monopoles: they are absent in the propagator of the singularity-free part of the gauge field. We assess carefully the Gribov copy problem for the propagator and the parameters emerging from the fits.
We study confinement and chiral symmetry breaking phase transitions for QCD and supersymmetric QCD. The method is based on some justified assumption regarding the behavior of the Green function relevant for the potential between two charges or a gap equation. We determine the number of flavors at which the transitions to confinement and chiral symmetry breaking take place. We find that whereas for chiral symmetry breaking the results are in perfect agreement with those in the literature for confinement the situation is more complex.
Green's functions are a central element in the attempt to understand non-perturbative phenomena in Yang-Mills theory. Besides the propagators, 3-point Green's functions play a significant role, since they permit access to the running coupling constant and are an important input in functional methods. Here we present numerical results for the two non-vanishing 3-point Green's functions in 3d pure SU(2) Yang-Mills theory in (minimal) Landau gauge, i.e. the three-gluon vertex and the ghost-gluon vertex, considering various kinematical regimes. In this exploratory investigation the lattice volumes…
This is the third lecture on quark confinement given by V.N.Gribov in 1992 in Orsay. An extensive discussion of the consequences of all this for the structure of the Green function can be found in [5,6] - in the two last papers concluding his 20 years long study of the problem of quark confinement in QCD. The text was prepared for publication by Yu. Dokshitzer, B. Metsch and J. Nyiri on the basis of a tape recording and notes taken during the lecture.
We present recent results for the Landau-gauge gluon and ghost propagators in SU(3) lattice gluodynamics obtained on a sequence of lattices with linear extension ranging from L=64 to L=96 at $β= 5.70$, thus reaching "deep infrared" momenta down to 75 MeV. Our gauge-fixing procedure essentially uses a simulated annealing technique which allows us to reach gauge-functional values closer to the global maxima than standard approaches do. Our results are consistent with the so-called decoupling solutions found for Dyson-Schwinger and functional renormalization group equations.
After a derivation of low-energy limit of QCD, being this a non-local Nambu-Jona-Lasinio model, we are able to show that confinement emerges as a two-loop correction to the gluon propagator. One-gluon exchange is not enough as recently shown in literature about studies on the gluon propagator in the Landau gauge.
The infrared behavior of Yang-Mills theory at finite temperature provides access to the role of confinement. In this review recent results on this topic from lattice calculations and especially Dyson-Schwinger studies are discussed. These indicate persistence of a residual confinement even in the high-temperature phase. The confinement mechanism is very similar to the one in the vacuum for the chromomagnetic sector. In the chromoelectric sector screening occurs at the soft scale g^2T, although not leading to a perturbative behavior.
The Gluon and Ghost propagators in Landau gauge QCD are investigated using the Schwinger-Dyson equation approach. Working in Euclidean spacetime, we solve for these propagators using a selection of vertex inputs, initially for the ghost equation alone and then for both propagators simultaneously. The results are shown to be highly sensitive to the choices of vertices. We favor the infrared finite ghost solution from studying the ghost equation alone where we argue for a specific unique solution. In order to solve this simultaneously with the gluon using a dressed-one-loop truncation, we find t…
The high-temperature phase of Yang-Mills theory in Landau gauge is studied using Dyson-Schwinger equations. The propagators of the gluon and the Faddeev-Popov ghosts are obtained at finite and infinite temperature, partially analytically. The results are in good agreement with lattice results. It is found that the infrared properties are only quantitatively affected by temperature. The confinement of at least soft gluons transverse to the heat bath is established, in accordance with the Kugo-Ojima and Gribov-Zwanziger confinement scenarios. This is confirmed by investigating the corresponding …
We study the properties of quarks, being confined in hadrons, with the Schwinger-Dyson equation in the dual Ginzburg-Landau Theory. Magnetic monopole condensation, which provides quark confinement, is demonstrated responsible also for dynamical chiral-symmetry breaking. We discuss then the recovery of the chiral symmetry at finite temperature.
Without any analytical assumption we solve the ladder QED2+1 in Minkowski space. Further, we transform Greens functions to the Temporal Euclidean space, wherein we show that in the special case of ladder QED2+1 the solution is fully equivalent to the Minkowski one. The obtained complex fermion propagator exhibits confinement because of the lack of the pole at the real timelike $q^2$ axis.
The ghost and gluon propagator and the ghost-gluon and three-gluon vertex of two-dimensional SU(2) Yang-Mills theory in (minimal) Landau gauge are studied using lattice gauge theory. It is found that the results are qualitatively similar to the ones in three and four dimensions. The propagators and the Faddeev-Popov operator behave as expected from the Gribov-Zwanziger scenario. In addition, finite volume effects affecting these Green's functions are investigated systematically. The critical infrared exponents of the propagators, as proposed in calculations using stochastic quantization and Dy…
The infrared behavior of gluon and ghost propagators offers a crucial test of confinement scenarios in Yang-Mills theories. A nonperturbative study of these propagators from first principles is possible in lattice simulations, but one must consider significantly large lattice sizes in order to approach the infrared limit. We propose constraints based on general properties of the propagators to gain control over the extrapolation of data to the infinite-volume limit. These bounds also provide a way to relate the propagators to simpler, more intuitive quantities. We apply our analysis to the cas…
We discuss the Casimir scaling hypothesis on the nonperturbative force in terms of the dual superconducting picture of the QCD vacuum by calculating the string tensions of flux tubes associated with static charges in various SU(3) representations in the dual Ginzburg-Landau (DGL) theory.
Due to the nonperturbative masslessness of the ghost field, ghost loops that contribute to gluon Green's functions in the Landau gauge display infrared divergences, akin to those one would encounter in a conventional perturbative treatment. This is in sharp contrast with gluon loops, in which the perturbative divergences are tamed by the dynamical generation of a gluon mass acting as an effective infrared cutoff. In this paper, after reviewing the full nonperturbative origin of this divergence in the two-gluon sector, we discuss its implications for the three- and four-gluon sector, showing in…
Without any analytical assumption we solve the ladder QED2+1 in Minkowski space. Further, we transform Greens functions to the Temporal Euclidean space, wherein we show that in the special case of ladder QED2+1 the solution is fully equivalent to the Minkowski one. QCD quark gap equation is solved in the framework of Temporal Euclidean space as well. In both models, the obtained complex fermion propagators exhibits confinement, since it does not satisfies Khallen-Lehmann representation.
Recent studies of QCD Green's functions and their applications in hadronic physics are reviewed. We briefly discuss the issues of gauge fixing, BRS invariance and positivity. Evidence for the violation of positivity by quarks and transverse gluons in the covariant gauge is collected, and it is argued that this is one manifestation of confinement. We summarise the derivation of the Dyson-Schwinger equations (DSEs) of QED and QCD. The influence of instantons on DSEs in a 2-dimensional model is mentioned. Solutions for the Green's functions in QED in 2+1 and 3+1 dimensions provide tests of variou…
The infrared behavior of the quark-gluon vertex of quenched Landau gauge QCD is studied by analyzing its Dyson-Schwinger equation. Building on previously obtained results for Green functions in the Yang-Mills sector we analytically derive the existence of power-law infrared singularities for this vertex. We establish that dynamical chiral symmetry breaking leads to the self-consistent generation of components of the quark-gluon vertex forbidden when chiral symmetry is forced to stay in the Wigner-Weyl mode. In the latter case the running strong coupling assumes an infrared fixed point. If chir…
We study abelian dominance and monopole condensation for the quark confinement physics using the lattice QCD simulations in the MA gauge. These phenomena are closely related to the dual superconductor picture of the QCD vacuum, and enable us to construct the dual Ginzburg-Landau (DGL) theory as an useful effective theory of nonperturbative QCD. We then apply the DGL theory to the studies of the low-lying hadron structure and the scalar glueball properties.
The results of different non-perturbative studies agree on a power law as the infrared behavior of the Landau gauge gluon propagator. This propagator violates positivity and thus indicates the absence of the transverse gluons from the physical spectrum, i.e. gluon confinement. A simple analytic structure for the gluon propagator is proposed capturing all of its features. We comment also on related investigations for the Landau gauge quark propagator.
We show that QCD Green functions in Landau Gauge exhibit sizable $O(1/μ^2)$ corrections to the expected perturbative behavior at energies as high as 10 GeV. We argue that these are due to a $<A^2>$-condensate which does not vanish in Landau gauge.
This is the second of the two last papers by V. N. Gribov concluding his 20 year long study of the problem of quark confinement in QCD. In this paper the analytic structure of quark and gluon Green's functions is investigated in the framework of the theory of confinement based on the phenomenon of supercritical binding of light quarks. The problem of unitarity in a confining theory is discussed. The write-up remained unfinished and so it is presented here. The author was planning to considerably extend the paper. The text was prepared for publication by Yu. Dokshitzer, C. Ewerz, and J. Nyiri.
We develop a calculational scheme in Coulomb and temporal gauge that respects gauge invariance and is most easily applied to the infrared asymptotic region of QCD. It resembles the Dyson-Schwinger equations of Euclidean quantum field theory in Landau gauge, but is 3-dimensional. A simple calculation yields a color-Coulomb potential that behaves at large $R$ approximately like $V_{\rm coul}(R) \sim R^{[1-0.2(d-1)]}$ for spatial dimension $1 \leq d \leq 3$. This is a linearly rising potential plus a rather weak dependence on $d$.
We study the effect of QCD-monopole condensation on the dynamical chiral-symmetry breaking by using the dual Ginzburg-Landau theory of QCD. We formulate the Schwinger-Dyson equation and solve it numerically. The large enhancement is found for the chiral-symmetry breaking due to QCD-monopole condensation, which suggests the close relation between the color confinement and the chiral-symmetry breaking.
The Coulomb gauge model of QCD is studied with the introduction of a confining potential into the scalar part of the vector potential. Using a Green function formalism, we derive the self-energy for this model, which has both scalar and vector parts, $Σ^S(p)$ and $Σ^V(p)$. A rotation of these variables leads to the so-called gap and energy equations. We then analyse the divergence structure of these equations. As this depends explicitly on the form of potential, we give as examples both the linear plus Coulomb and quadratically confining potentials. The nature of the confining single particle …
We study three subjects on quark confinement in hadrons in SU(3)$_{\rm c}$ lattice QCD. From the accurate lattice calculation for more than 300 different patterns of three-quark (3Q) systems, we find that the static 3Q potential is well described by Y-Ansatz, i.e., the Coulomb plus Y-type linear potential. We also study the multi-quark (4Q, 5Q) potentials in lattice QCD, and find that they are well described by the one-gluon-exchange (OGE) Coulomb plus string-theoretical linear potential, which supports the {\it infrared string picture} even for the multi-quarks. The second subject is a lattic…
In lattice QCD the computation of one-particle irreducible (1PI) Green's functions with a large number (> 2) of legs is a challenging task. Besides tuning the lattice spacing and volume to reduce finite size effects, the problems associated with the estimation of higher order moments via Monte Carlo methods and the extraction of 1PI from complete Green's functions are limitations of the method. Herein, we address these problems revisiting the calculation of the three gluon 1PI Green's function.
We study the properties of the QCD vacuum in the dual Ginzburg-Landau theory, where QCD-monopole condensation leads to the linear confinement potential. Using the effective potential, we find monopole dominance for chiral-symmetry breaking. The effective mass of off-diagonal (charged) gluons is estimated as $M_{ch} \simeq 1.31$ GeV. The gluon condensate is calculated as $<\frac{α_{s}}πG^2 > = (344 MeV)^4$.
We study the relation between QCD-monopole condensation and dynamical chiral-symmetry breaking in the dual Ginzburg-Landau Theory, which realizes the color confinement due to the dual Meissner effect. Solving the Schwinger-Dyson equation at finite temperature numerically, we find the chiral symmetry is restored at high temperature. The critical temperature of the chiral symmetry restoration is strongly correlated with the string tension.
Recently there has been progress in the understanding of the confinement mechanism in Landau gauge QCD. The emerging dynamical description in terms of the underlying gauge dependent degrees of freedom goes beyond the static confinement in the quenched limit and has the potential to describe the scale-dependent phenomenon seen in nature, where new hadrons are produced when the system is sufficiently excited. I point out that the confinement mechanism for quarks is rather different from the corresponding one for gluons and that both are embedded in a consistent framework that can describe import…
We discuss the properties of ghost and gluon propagators in Landau gauge Yang-Mills theory and their relation to the confinement problem. In general two types of infrared behavior of these functions are allowed from their functional equations: scaling and decoupling. Both solutions show positivity violations in the gluon propagator and lead to a confining Polyakov loop potential. However, only the scaling solution agrees with the Kugo-Ojima confinement scenario and the related formulation of a physical Hilbert space of Yang-Mills theory. Our numerical results for the gluon dressing function ag…
We study the masses and the leptonic decay widths of heavy quarkonium in the dual Ginzburg-Landau (DGL) theory of QCD, in which the abelian monopole condensation plays an essential role for color confinement. The effect of color screening due to the light quark pair creation is introduced by the infrared momentum cutoff in the gluon propagator. We find that the color screening effect is important to reproduce the properties of the heavy quarkonium, in particular the leptonic decay width. We also discuss the underlying systematics of the heavy quark spectroscopy in the DGL theory.
It is a long-standing question whether the confinement of matter fields in QCD has an imprint in the (gauge-dependent) correlation functions, especially the propagators. In particular in the quenched case a fundamental difference could be expected between adjoint and fundamental matter. In a preceding investigation the propagator of a fundamental scalar has been studied, showing no obvious sign of confinement. Here, complementary, the adjoint scalar propagator is investigated over a wide range of parameters in the minimal Landau gauge using lattice gauge theory. This study is performed in two,…
The infrared behavior of the gluon propagator is directly related to confinement in QCD. Indeed, the Gribov-Zwanziger scenario of confinement predicts an infrared vanishing (transverse) gluon propagator in Landau-like gauges, implying violation of reflection positivity and gluon confinement. Finite-volume effects make it very difficult to observe (in the minimal Landau gauge) an infrared suppressed gluon propagator in lattice simulations of the four-dimensional case. Here we report results for the SU(2) gluon propagator in a gauge that interpolates between the minimal Landau gauge (for gauge p…
We briefly review the QCD physics and then introduce recent topics on the confinement physics. In the maximally abelian (MA) gauge, the low-energy QCD is abelianized owing to the effective off-diagonal gluon mass $M_{\rm off} \simeq 1.2 {\rm GeV}$ induced by the MA gauge fixing. We demonstrate the construction of the dual Ginzburg-Landau (DGL) theory from the low-energy QCD in the MA gauge in terms of the lattice QCD evidences on infrared abelian dominance and infrared monopole condensation.
