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Kei-Ichi Kondo

Publications and source records attributed to Kei-Ichi Kondo.

At least 91 records · Page 5Linked to original sources
arXiv2012

Quark confinement due to non-Abelian magnetic monopoles in SU(3) Yang-Mills theory

We present recent results on quark confinement: in SU(3) Yang-Mills theory, confinement of fundamental quarks is obtained due to the dual Meissner effect originated from non-Abelian magnetic monopoles defined in a gauge-invariant way, which is distinct from the well-known Abelian projection scenario. This is achieved by using a non-Abelian Stokes theorem for the Wilson loop operator and a new reformulation of the Yang-Mills theory.

hep-th↗
arXiv2012

Dual Meissner effect and non-Abelian dual superconductivity in SU(3) Yang-Mills theory

The dual Meissner effect is the promising mechanism for quark confinement. We have proposed a new formulation of SU(N) Yang-Mills (YM) theory on a lattice, which can extract the dominant mode for quark confinement in the gauge independent manner. In the last lattice conference, we have demonstrated by measuring the string tension from the Wilson loop average in the SU(3) YM theory that the restricted non-Abelian variable and the extracted non-Abelian magnetic monopoles play the dominant role in confinement of fundamental quarks (dominance in the string tension), in marked contrast to the Abelian projection. In this talk, we focus on the dual Meissner effect in SU(3) YM theory, which is examined by measuring the distribution of chromo-electric field strength created by a static quark-antiquark pair. We apply the new lattice formulation, and examine whether or not the non-Abelian dual superconductivity claimed by us is indeed a mechanism of quark confinement. We present a preliminary result of the direct evidence for the non-abelian dual Meissner effect, that is to say, restricted U(2)-field part of the flux tube plays the dominant role in the quark-antiquark potential.

hep-lat↗
arXiv2012

A unitary and renormalizable model for massive Yang-Mills fields without Higgs fields

We propose a massive Yang-Mills model blessed with both physical unitarity and renormalizability without Higgs particles. This is achieved by a novel nonlinear but local transformation from the original fields in the Curci-Ferrari model to the massive vector field with the spin one, which has the correct physical degrees of freedom and invariant under an extended BRST transformation. We clarify the reason for failures of the preceding attempts and check the physical unitarity in perturbation theory.

hep-th↗
arXiv2011

Quark and gluon confinement from an effective model of Yang-Mills theory

We derive a gauge-invariant low-energy effective model of the SU(2) Yang-Mills theory. We find that the effective gluon propagator belongs to the Gribov-Stingl type, irrespective of the gauge choice. In the maximally Abelian gauge, especially, we demonstrate that the model exhibits both quark confinement and gluon confinement: the Wilson loop average has area law and the Schwinger function violates reflection positivity. Moreover, we give a formula for the string tension calculable from the gluon propagator of the gauge-invariant field strength and gives a good estimate for the string tension. We discuss if quark confinement and gluon confinement are of the same origin attributed to the gluon propagator in the deep infrared momentum region.

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arXiv2011

A low-energy effective Yang-Mills theory for quark and gluon confinement

We derive a gauge-invariant low-energy effective model of the Yang-Mills theory. We find that the effective gluon propagator belongs to the Gribov-Stingl type and agrees with it when a mass term which breaks nilpotency of the BRST symmetry is included. We show that the effective model with gluon propagator of the Gribov-Stingl type exhibits both quark and gluon confinement: the Wilson loop average has the area law and the Schwinger function violates reflection positivity. However, we argue that both quark and gluon confinement can be obtained even in the absence of such a mass term.

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arXiv2010

Toward a first-principle derivation of confinement and chiral-symmetry-breaking crossover transitions in QCD

We give a theoretical framework to obtain a low-energy effective theory of quantum chromodynamics (QCD) towards a first-principle derivation of confinement/deconfinement and chiral-symmetry breaking/restoration crossover transitions. In fact, we demonstrate that an effective theory obtained using simple but non-trivial approximations within this framework enables us to treat both transitions simultaneously on equal footing. A resulting effective theory is regarded as a modified and improved version of nonlocal Polyakov-loop extended Nambu-Jona-Lasinio (nonlocal PNJL) models proposed recently by Hell, Rössner, Cristoforetti and Weise, and Sasaki, Friman and Redlich, extending the original (local) PNJL model by Fukushima and others. A novel feature is that the nonlocal NJL coupling depends explicitly on the temperature and Polyakov loop, which affects the entanglement between confinement and chiral symmetry breaking, together with the cross term introduced through the covariant derivative in the quark sector considered in the conventional PNJL model. The chiral symmetry breaking/restoration transition is controlled by the nonlocal NJL interaction, while the confinement/deconfinement transition in the pure gluon sector is specified by the nonperturbative effective potential for the Polyakov loop obtained recently by Braun, Gies, Marhauser and Pawlowski. The basic ingredients are a reformulation of QCD based on new variables and the flow equation of the Wetterich type in the Wilsonian renormalization group. This framework can be applied to investigate the QCD phase diagram at finite temperature and density.

hep-th↗
arXiv2010

Jackiw-Nohl-Rebbi two-instanton as a source of magnetic monopole loop

We demonstrate that a Jackiw-Nohl-Rebbi solution as the most general two-instanton generates a circular loop of magnetic monopole in four-dimensional Euclidean SU(2) Yang-Mills theory, in contrast to the one-instanton solution in the regular gauge for which no such magnetic monopole loops exist. These results together with our previous result indicate that two-instanton solution and two-meron solution with the same asymptotic behavior in the long distance are responsible for quark confinement based on the dual superconductivity picture.

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arXiv2009

The exact decomposition of gauge variables in lattice Yang-Mills theory

In this paper, we consider lattice versions of the decomposition of the Yang- Mills field a la Cho-Faddeev-Niemi, which was extended by Kondo, Shinohara and Murakami in the continuum formulation. For the SU(N) gauge group, we propose a set of defining equations for specifying the decomposition of the gauge link variable and solve them exactly without using the ansatz adopted in the previous studies for SU(2) and SU(3). As a result, we obtain the general form of the decomposition for SU(N) gauge link variables and confirm the previous results obtained for SU(2) and SU(3).

hep-lat↗
arXiv2009

Topological configurations of Yang-Mills field responsible for magnetic-monopole loops as quark confiner

We have given a new description of the lattice Yang-Mills theory a la Cho-Faddeev-Niemi-Shabanov, which has enabled us to confirm in a gauge-independent manner "Abelian"-dominance and magnetic-monopole dominance in the Wilson loop average, yielding a gauge-independent dual superconductor picture for quark confinement. In particular, we have given a new procedure (called reduction) for obtaining a gauge-independent magnetic monopole from a given Yang-Mills field. In this talk, we demonstrate how some of known topological configurations in the SU(2) Yang-Mills theory such as merons and instantons generate closed loops of magnetic-monopole current as the quark confiner, both of which are characterized by the gauge-invariant topological index, topological charge (density) and magnetic charge (density), respectively. We also try to detect which type of topological configurations exist in the lattice data involving magnetic-monopole loops generated by Monte Carlo simulation. Here we apply a new geometrical algorithm based on "computational homology" to discriminating each closed loop from clusters of magnetic-monopole current, since the magnetic-monopole current on a lattice is integer valued.

hep-lat↗
arXiv2009

Gribov-Zwanziger horizon condition, ghost and gluon propagators and Kugo-Ojima confinement criterion

We reexamine the conventional arguments concerned with the scaling and decoupling solutions for the ghost and gluon propagators in the Landau gauge Yang-Mills theory. We point out a few issues to be clarified, which seems to be overlooked in the previous investigations in this field, in the fully non-perturbative treatment. We propose a trick which enables one to incorporate the Gribov horizon directly into the self-consistent Schwinger-Dyson equation in the gauge-fixed Yang-Mills theory, using the Gribov-Zwanziger framework with the horizon term. We obtain the following results, irrespective of the choice of the horizon term. (i) We find that there exists a family of solutions parameterized by one-parameter $w_R(0)$ which was assumed to be zero implicitly. The family includes both the scaling and decoupling solutions, and specification of the parameter discriminates between them. (ii) We observe that the inclusion of the horizon term cancels the ultraviolet divergence in the Schwinger-Dyson equation for the ghost propagator and the resulting (non-perturbative) self-consistent solution becomes ultraviolet finite. In other words, the horizon condition interpolates between the infrared behavior and the ultraviolet one. This leads to the incompatibility of the conventional multiplicative renormalization scheme with the Gribov

hep-th↗
arXiv2009

Decoupling and scaling solutions in Yang-Mills theory with the Gribov horizon

We propose a trick which enables one to incorporate the Gribov horizon into the Schwinger-Dyson equation in Landau and Coulomb gauge Yang-Mills theory, using the Gribov-Zwanziger framework with the horizon term. We find a family of solutions parameterized by one-parameter $w_R(0)$ which was overlooked so far by assuming to be zero implicitly. The family includes both the scaling and decoupling solutions, and specification of the parameter discriminates between them. In the Landau gauge we discuss a possible decoupling solution satisfying the Kugo-Ojima criterion for color confinement.

hep-th↗
arXiv2009

Infrared behavior of the ghost propagator in the Landau gauge Yang-Mills theory

We prove that the Faddeev-Popov ghost dressing function in the Yang-Mills theory is non-zero and finite in the limit of vanishing momenta and hence the ghost propagator behaves like free in the deep infrared regime, within the Gribov-Zwanziger framework of the $D$-dimensional SU(N) Yang-Mills theory in the Landau gauge for any $D>2$. This result implies that the Kugo-Ojima color confinement criterion is not satisfied in its original form. We point out that the result crucially depends on the explicit form of the non-local horizon term adopted. The original Gribov prediction in the Landau gauge should be reconsidered in connection with color confinement.

hep-th↗
arXiv2009

Kugo-Ojima color confinement criterion and Gribov-Zwanziger horizon condition

We rewrite the Zwanziger horizon condition in terms of the Kugo-Ojima parameter for color confinement. This enables one to explain which value of the Kugo-Ojima parameter is allowed if the horizon condition is imposed. Although all the calculations are performed in the limit of vanishing Gribov parameter for simplicity, the obtained value is consistent with the result of numerical simulations. Consequently, the ghost propagator behaves like free and the gluon propagator is non-vanishing at low momenta, in harmony with recent lattice results and decoupling solution of the Schwinger-Dyson equation. The Kugo-Ojima criterion is realized only when the restriction is removed.

hep-th↗
arXiv2009

The nilpotent "BRST" symmetry for the Gribov-Zwanziger theory

We have found a nilpotent quantum symmetry of Yang-Mills theory restricted to the Gribov region. In fact, we give a set of transformations for the filds a la BRST that leaves the Gribov-Zwanziger action invariant and obeys the nilpotency, although the usual BRST symmetry is broken due to the non-vanishing Gribov parameter representing the presence of the Gribov horizon in the configuration space of the Yang-Mills field. We show that the horizon condition (the gap equation determining the Gribov parameter) follows from the modified BRST invariance of the vacuum.

hep-th↗
arXiv2008

Magnetic monopole loops supported by a meron pair as the quark confiner

We give a definition of gauge-invariant magnetic monopoles in Yang-Mills theory without using the Abelian projection due to 't Hooft. They automatically appear from the Wilson loop operator. This is shown by rewriting the Wilson loop operator using a non-Abelian Stokes theorem. The magnetic monopole defined in this way is a topological object of co-dimension 3, i.e., a loop in four-dimensions. We show that such magnetic loops indeed exist in four-dimensional Yang-Mills theory. In fact, we give an analytical solution representing circular magnetic monopole loops joining a pair of merons in the four-dimensional Euclidean SU(2) Yang-Mills theory. This is achieved by solving the differential equation for the adjoint color (magnetic monopole) field in the two--meron background field within the recently developed reformulation of the Yang-Mills theory. Our analytical solution corresponds to the numerical solution found by Montero and Negele on a lattice. This result strongly suggests that a meron pair is the most relevant quark confiner in the original Yang-Mills theory, as Callan, Dashen and Gross suggested long ago.

hep-th↗
arXiv2008

A new description of lattice Yang-Mils theory and non-Abelian monopoles as the quark confiner

We propose a new description of the SU(N) Yang-Mills theory on a lattice, which enables one to explain quark confinement based on the dual superconductivity picture in a gauge independent way. This is because we can define gauge-invariant magnetic monopoles which are inherent in the Wilson loop operator. For SU(3) there are two options: the minimal option with a single type of non-Abelian magnetic monopole characterized by the maximal stability subgroup $\tilde{H}=U(2)=SU(2)\times U(1)$, and the maximal one with two types of Abelian magnetic monopoles characterized by the maximal torus subgroup $\tilde{H}=U(1)\times U(1)$. The maximal option corresponds to a gauge independent reformulation of the Abelian projection represented by the conventional MAG. In the minimal option, we have successfully performed the numerical simulation of the SU(3) Yang-Mills theory on a lattice. We give preliminary numerical results showing the dominance of the non-Abelian magnetic monopole in the string tension obtained from the Wilson loop in the fundamental representation, and the infrared dominance of a decomposed field variable for correlation functions after demonstrating the preservation of color symmetry which was explicitly broken by the conventional MAG.

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