Violation of non-Abelian Bianchi identity can be regarded as $N^2-1$ Abelian-like monopole currents in the continuum SU(N) QCD. Three Abelian-like monopoles, when defined in SU(2) gluodynamics on the lattice à la DeGrand-Toussaint, are shown to have the continuum limit with respect to the color-invariant monopole density and the effective monopole action. Since each Abelian-like monopole is not gauge invariant, we have introduced various partial gauge fixing for the purpose of reducing lattice artifact monopoles in the thermalized vacuum. Here we investigate Abelian and monopole dominances and the Abelian dual Meissner effects adopting the same gauges like the maximal center gauge (MCG) in comparison with the maximal Abelian gauge (MAG). Abelian and monopole contributions to the string tension in these gauges are observed to be a little smaller than the non-Abelian string tension. However, we find that the monopole dominance is improved well when use is made of the block-spin transformations with respect to Abelian-like monopoles. We find each electric field is squeezed by the corresponding colored Abelian-like monopole in such gauges and the Abelian dual Meissner effect is observed independently for each color. Moreover, we confirm the dual Ampère's law in these new gauges as well as in MAG. The SU(2) vacuum is shown to be near the border between the type 1 and type 2 dual superconductors. The penetration length is almost equal for the four gauge fixings and the vacuum type in MCG is almost the same value as the previous results. These results are consistent with the previous results suggesting the continuum limit and the gauge-independence of Abelian monopoles.
The dual Meissner effect is observed without monopoles in quenched SU(2) QCD with Landau gauge-fixing. Abelian as well as non-Abelian electric fields are squeezed. Magnetic displacement currents which are time-dependent Abelian magnetic fields play a role of solenoidal currents squeezing Abelian electric fields. Monopoles are not always necessary to the dual Meissner effect. The squeezing of the electric flux means the dual London equation and the massiveness of the Abelian electric fields as an asymptotic field. The mass generation of the Abelian electric fields is related to a gluon condensa…
In the $SU(2)$ Yang-Mills theory on the four-dimensional Euclidean lattice, we confirm the gauge-independent "Abelian" dominance (or the restricted field dominance) and gauge-independent magnetic-monopole dominance in the string tension of the linear potential extracted from the Wilson loop in the fundamental representation. The dual Meissner effect is observed by demonstrating the squeezing of the chromoelectric field flux connecting a pair of quark and antiquark. In addition, the circular magnetic-monopole current is induced around the chromoelectric flux. The type of the dual superconductiv…
Performing highly precise Monte-Carlo simulations of SU(2) gluodynamics, we observe for the first time Abelian dominance in the confining part of the static potential in local unitary gauges such as the F12 gauge. We also study the flux-tube profile between the quark and antiquark in these local unitary gauges and find a clear signal of the dual Meissner effect. The Abelian electric field is found to be squeezed into a flux tube by the monopole supercurrent. This feature is the same as that observed in the non-local maximally Abelian gauge. These results suggest that the Abelian confinement sc…
After making an abelian projection in the maximally abelian gauge, we measure the distribution of abelian electric flux and monopole currents around an abelian Wilson loop in $SU(2)$ and $SU(3)$ QCD. The (dual) Meissner effect is observed clearly. The vacua in the confinement phases of $SU(2)$ and $SU(3)$ are both at around the border between type-1 and type-2 (dual) superconductor.
The dual superconductivity is a promising mechanism for quark confinement. We proposed the non-Abelian dual superconductivity picture for SU(3) Yang-Mills theory, and demonstrated the restricted field dominance (called conventionally "Abelian" dominance), and non-Abelian magnetic monopole dominance in the string tension. In the last conference, we have demonstrated by measuring the chromoelectric flux that the non-Abelian dual Meissner effect exists and determined that the dual superconductivity for SU(3) case is of type I, which is in sharp contrast to the SU(2) case: the border of type I and…
The dual Meissner effect is described and numerically observed in a gauge-invariant way in lattice Monte-Carlo simulations of pure SU(2) QCD. A gauge-invariant Abelian-like field strength is defined in terms of a unit-vector in color space which is constructed by a non-Abelian field strength itself. A gauge-invariant monopole-like quantity is defined by a violation of the Bianchi identity with respect to the Abelian-like field strength. The squeezing of the non-Abelian electric field $\sqrt{\sum_a(E^a_i)^2}$ between a pair of static quark and anti-quark occurs due to the solenoidal current com…
The mechanism of non-Abelian color confinement is studied in SU(2) lattice gauge theory in terms of the Abelian fields and monopoles extracted from non-Abelian link variables without adopting gauge fixing. Firstly, the static quark-antiquark potential and force are computed with the Abelian and monopole Polyakov loop correlators, and the resulting string tensions are found to be identical to the non-Abelian string tension. These potentials also show the scaling behavior with respect to the change of lattice spacing. Secondly, the profile of the color-electric field between a quark and an antiq…
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 Abeli…
The dual Meissner effect is described and numerically observed in a gauge-invariant way in lattice Monte-Carlo simulations in pure SU(2) QCD. The squeezing of the non-Abelian electric field between a pair of static quark and anti-quark occurs due to the solenoidal current coming from the gauge-invariant monopole-like quantity. Preliminary results are obtained with respect to the vacuum type of the confinement phase. The SU(2) QCD vacuum seems near the border between the type 1 and the type 2 dual superconductors. The theoretical background of this idea is published in another report \cite{Suzu…
We demonstrate that confinement in $SU(2)$ gauge theory is produced by dual superconductivity of the vacuum. We show that for $T < T_c$ (temperature of deconfining phase transition) the $U(1)$ symmetry related to monopole charge conservation is spontaneously broken; for $T > T_c$ the symmetry is restored.
We study the distribution of the color fields due to a static quark-antiquark pair in SU(2) lattice gauge theory. We find that the London penetration length measured after Abelian projection in the Abelian Covariant gauge (Maximal Abelian gauge) agrees with the one obtained without gauge fixing. Moreover the penetration length scales according to asymptotic freedom. We put out a simple relation between the penetration length and the string tension.
We have proposed the non-Abelian dual superconductivity picture for quark confinement in the SU(3) Yang-Mills (YM) theory, and have given numerical evidences for the restricted-field dominance and the non-Abelian magnetic monopole dominance in the string tension by applying a new formulation of the YM theory on a lattice. To establish the non-Abelian dual superconductivity picture for quark confinement, we have observed the non-Abelian dual Meissner effect in the SU(3) Yang-Mills theory by measuring the chromoelectric flux created by the quark-antiquark source, and the non-Abelian magnetic mon…
We have presented non-Abelian dual superconductivity picture in the SU(3) Yang-Mills(YM) theory, and shown evidences such as the restricted U(2)-field dominance and the non-Abelian magnetic monopole dominance in the string tension. To establish the dual superconductivity picture, the dual Meissner effect in Yang-Mills theory must be examined, and we also presented the evidence of non-Abelian dual Meissner effect by measuring chromo-electric flux tube in the last lattice conferences. In this talk, by applying a new formulation of the YM theory on a lattice, the we further investigate the non-Ab…
The dual Meissner effect is observed without monopoles in quenched $SU (2)$ QCD with Landau gauge-fixing. Magnetic displacement currents which are time-dependent Abelian magnetic fields play a role of solenoidal currents squeezing Abelian electric fields. Monopoles are not always necessary to the dual Meissner effect. The squeezing of the electric flux means the dual London equation and the massiveness of the Abelian electric fields as an asymptotic field. The mass generation of the Abelian electric fields is related to a gluon condensate $<A^a_μA^a_μ>\neq 0$ of mass dimension 2.
The dual superconductivity is a promising mechanism for quark confinement. We have proposed the non-Abelian dual superconductivity picture for SU(3) Yang-Mills theory, and showed the restricted field dominance (called conventionally Abelian dominance), and non-Abelian magnetic monopole dominance in the string tension. We have further demonstrated by measuring the chromoelectric flux that the non-Abelian dual Meissner effect exists and determined that the dual superconductivity for SU(3) case is of type I, which is in sharp contrast to the SU(2) case: the border of type I and type II. In this t…
Using the renormalization group motivated smoothing technique, the large scale structure of lattice configurations at finite temperature is characterized in terms of Abelian monopoles identified in the maximally Abelian, the Laplacian Abelian, and the Polyakov gauge. Abundance and anisotropy of monopoles at deconfinement and gauge invariant properties like local non-Abelian action and topological density are studied. Monopoles are predominantly found in regions of large action and topological charge, rather independent of the chosen gauge.
A comparative study of Abelian and Monopole dominance in the Laplacian and Maximally Abelian projected gauges is carried out. Clear evidence for both types of dominance is obtained for the Laplacian projection. Surprisingly, the evidence is much more ambiguous in the Maximally Abelian gauge. This is attributed to possible ``long-distance imperfections'' in the maximally abelian gauge fixing.
Using a renormalization group motivated smoothing technique, we investigate the large scale structure of lattice configurations at finite temperature, concentrating on Abelian monopoles identified in the maximally Abelian, the Laplacian Abelian, and the Polyakov gauge. Monopoles are mostly found in regions of large action and topological charge, rather independent of the gauge chosen to detect them. Gauge invariant properties around Abelian monopoles, the local non-Abelian action and topological density, are studied. We show that the local averages of these densities along the monopole traject…
We study Abelian monopole and vortex condensation in lattice pure gauge theories. Condensation is detected by means of a disorder parameter defined in terms of a gauge-invariant effective action introduced using the lattice Schrödinger functional. Dirac monopoles condense in the confined phase of U(1) lattice gauge theory. Abelian monopoles and Abelian vortices condense in the confined phase of SU(2) and SU(3) lattice gauge theories.
In this paper the properties of thermal Abelian monopoles in the deconfinement phase of the SU(2) gluodynamics are considered. In particular, to study the properties of the Abelian monopole component of QGP we calculate three-point correlation functions of monopoles for different temperatures from the region $T/T_c \in (1.5, 6.8)$. The results of the calculation show that the three-point correlation functions can be described by independent pair correlations of monopoles. From this one can conclude that the system of Abelian monopoles in QGP reveals the properties of a dilute gas. In addition,…
We investigate the dynamics of lattice gauge theories in an Abelian monopole background field. By means of the gauge-invariant lattice Schrodinger functional we study the Abelian monopole condensation in U(1) lattice gauge theory at zero temperature and in SU(3) lattice gauge theory at finite temperature.
The properties of the thermal abelian monopoles are studied in the deconfinement phase of the SU(2) gluodynamics. To remove effects of Gribov copies the simulated annealing algorithm is applied to fix the maximally abelian gauge. Computing the density of the thermal abelian monopoles in the temperature range between 1.5T_c and 6.9T_c we show, by comparison with earlier results, that the Gribov copies effects might be as high as 20% making proper gauge fixing mandatory. We find that in the infinite temperature limit the monopole density converges to its value in 3-dimensional theory. To study t…
As a color confinement mechanism, a dual Meissner effect due to Abelian monopoles involved in QCD has been discussed so far in various ways. But still there is an important problem unsolved. It is gauge invariance of the schemes or, in other words, the reason why non-Abelian color confinement is explained by means of the Abelian dual Meissner effect. Here it is shown that a random Abelian method based on the violation of non-Abelian Bianchi identity (VNABI) could prove SU(3) invariance and explain why color-singlets alone can survive in the confinement phase of QCD in the framework of the Abel…
We have pointed out that the $SU(3)$ Yang-Mills theory has a new way of reformulation using new field variables (minimal option), in addition to the conventional option adopted by Cho, Faddeev and Niemi (maximal option). The reformulation enables us to change the original non-Abelian gauge field into the new field variables such that one of them called the restricted field gives the dominant contribution to quark confinement in the gauge-independent way. In the minimal option, especially, the restricted field is non-Abelian $U(2)$ and involves the non-Abelian magnetic monopole. In the precedin…
Renormalization group (RG) smoothing is employed on the lattice to investigate and to compare the monopole structure of the SU(2) vacuum as seen in different gauges (maximally Abelian (MAG), Polyakov loop (PG) and Laplacian gauge (LG)). Physically relevant types of monopoles (LG and MAG) are distinguished by their behavior near the deconfining phase transition. For the LG, Abelian projection reproduces well the gauge independent monopole structure encoded in an auxiliary Higgs field. Density and localization properties of monopoles, their non-Abelian action and topological charge are studied. …
We study the continuum limit of the length spectrum of magnetic monopole structures found after various Abelian projections of pure gauge SU(2), including the maximally Abelian gauge. We comment on Gribov copies, and measurements of the string tension.
We study the structure of the isolated static monopoles in the maximal Abelian projection of SU(2) lattice gluodynamics. Our estimation of the monopole radius is $ \approx 0.06 fm$.
We study monopoles and gluon fields in QCD in the maximally abelian (MA) gauge in the context of the dual superconductor picture for confinement. In the abelian gauge, unit-charge magnetic monopoles appear, but multi-charge monopoles do not in general cases. The appearance of the monopole is studied using the gauge-connection formalism in relation to the SU($N_c$) singular gauge transformation. The relevant role of off-diagonal gluons is found for the appearance of monopoles in the abelian gauge in QCD. We study the gluon-field properties around the monopole in the MA gauge in terms of the act…
The properties of the thermal Abelian monopoles are studied in the deconfinement phase of the SU(2) gluodynamics. To remove effects of Gribov copies the simulated annealing algorithm is applied to fix the maximally Abelian gauge. To study monopole profile we complete the first computations of excess of the nonabelian action density as a function of the distance from the center of the thermal Abelian monopole. We have found that starting from the distances $\approx$ 2 lattice spacings the chromoelectric and chromomagnetic action densities created by monopole are equal to each other, from what w…
We formulate a stochastic gauge fixing method to study the gauge dependence of Abelian projection. In this method, one can change the gauge from the maximally Abelian one to no gauge fixing continuously. We have found that the linear part of the heavy quark potential from Abelian contribution depends little on the gauge parameter. Similar results have been obtained for the monopole contribution part.We also investigate the gauge dependence of the length of monopole loop, which is known to be important for the confinement, and monopole density. These results suggest that the picture that monopo…
Three topics about monopole dynamics after abelian projection are reported. The first is the new and detailed analyses of $SU(2)$ monopole action obtained after the block-spin transformation on the dual lattice. The $b=na(β)$ dependence for all couplings are well fitted with a universal curve. The distance dependence of the couplings is well reproduced by a massive propagator with the mass $m=0.8$ in unit of $b$. The second is the $SU(3)$ monopole action recently obtained. The third is new interesting gauges showing abelian and monopole dominances as in the maximally abelian gauge.
We investigate the Abelian monopole condensation in finite temperature SU(2) and SU(3) pure lattice gauge theories. To this end we introduce a gauge invariant disorder parameter built up in terms of the lattice Schrödinger functional. Our numerical results show that the disorder parameter is different from zero and Abelian monopole condense in the confined phase. On the other hand our numerical data suggest that the disorder parameter tends to zero, in the thermodynamic limit, when the gauge coupling constant approaches the critical deconfinement value. In the case of SU(3) we also compare the…
The properties of the thermal Abelian color-magnetic monopoles in the maximally Abelian gauge are studied in the deconfinement phase of the lattice SU(2) gluodynamics. To check universality of the monopole properties we employ the tadpole improved Symanzik action. The simulated annealing algorithm combined with multiple gauge copies is applied for fixing the maximally Abelian gauge to avoid effects of Gribov copies. We compute the density, interaction parameters, thermal mass and chemical potential of the thermal Abelian monopoles in the temperature range between Tc and 3Tc. In comparison with…
Extended Abelian monopoles are investigated in SU(2) lattice gauge theory in three dimensions. Monopoles are computed by Abelian projection in several gauges, including the maximal Abelian gauge. The number $N_m$ of extended monopoles in a cube of size $m^3$ (in lattice units) is defined as the number of elementary ($1^3$) monopoles minus antimonopoles in the cube ($m=1,2,\ldots$). The distribution of $1^3$ monopoles in the nonlocal maximal Abelian gauge is shown to be essentially random, while nonscaling of the density of $1^3$ monopoles in some local gauges, which has been previously observe…
We explore the analogy between quark confinement and the Meissner effect in superconductors. We measure the response of color-magnetic "supercurrents" from Dirac magnetic monopoles to the presence of a static quark-antiquark pair in four dimensional U(1) lattice gauge theory. Our results indicate that in the confined phase these currents screen the color-electric flux due to the quarks in an electric analogy of the Meisner effect. We show that U(1) lattice guage theory obeys both a dual London equation and an electric fluxoid quantization condition.
We investigate the masses of 0+ and 2+ glueballs in SU(2) lattice gauge theory using abelian projection to the maximum abelian gauge. We calculate glueball masses using both abelian links and monopole operators. Both methods reproduce the known full SU(2) results quantitatively. Positivity problems present in the abelian projection are discussed. We study the dependence of the glueball masses on magnetic current loop size, and find that the 0+ state requires a much greater range of sizes than does the 2+ state.
Based on the dual Higgs picture for confinement, we study monopole properties in the maximally abelian (MA) gauge using the lattice QCD. The monopole carries a large fluctuation of the gluon field and provides a large abelian action in abelian projected QCD (AP-QCD). We find large cancellation between abelian part and off-diagonal part of the action density around the monopole, which ensures the appearance of monopoles. The monopole in the MA gauge can be regarded as the collective mode of the large gluon fluctuation concentrated into the abelian sector, and would be relevant degrees of freedo…
In the maximally Abelian gauge of SU(2), the clusters of monopole current are found to divide into two distinct classes. The largest cluster permeates the lattice, has a density that scales and produces the string tension. The remaining clusters possess an approximate 1/l^3 number density distribution (l is the cluster length), their radii vary as \sqrt l and their total current density does not scale. Their contribution to the string tension is compatible with being exactly zero. Their number density can be thought of as arising from an underlying scale invariant distribution. This suggests t…
We perform lattice Monte-Carlo simulations of pure SU(2) QCD using the multi-level method. We find Abelian dominance in local unitary gauges such as those diagonalizing a plaquette. A static potential described by Abelian link fields alone gives us the same string tension as that of a non-Abelian potential. Abelian dominance of the string tension and Abelian flux tube profiles are observed also without gauge-fixing, i.e., without any Abelian projection. On the basis of these results, we propose a simple gauge-independent Abelian confinement scenario without any Abelian projection. All color co…
We describe numerical calculation results for the probability distribution of the value of the monopole creation operator in the SU(2) lattice gluodynamics. We work in the maximal abelian projection. It occurs that at low temperatures, below the deconfinement phase transition, the maximum of the distribution is shifted from zero, which means that the effective constraint potential is of the Higgs type. Above the phase transition the minimum of the potential (the maximum of the monopole field distribution) is at the zero value of the monopole field. This fact confirms the existence of the abeli…
Using the SU(2) lattice QCD, we formulate the dual Wilson loop and study the dual Higgs mechanism induced by monopole condensation in the maximally abelian (MA) gauge, where QCD is reduced into an abelian gauge theory including the electric current $j_μ$ and the monopole current $k_μ$. After the abelian projection in the MA gauge, the system can be separated into the photon part and the monopole part corresponding to the separation of $j_μ$ and $k_μ$, respectively. We study here the monopole part (the monopole-current system), which is responsible to the electric confinement. Owing to the abse…
An effective monopole action is derived from vacuum configurations after abelian projection in the maximally abelian gauge in $SU(2)$ QCD. Entropy dominance over energy of monopole loops is seen on the renormalized lattice with the spacing $b>b_c\simeq 5.2\times10^{-3} Λ_L^{-1}$ when the physical volume of the system is large enough. QCD confinement may be interpreted as the (dual) Meissner effect due to the monopole condensation.
The dual superconductivity is a promising mechanism of quark confinement. In the preceding works, we have given a non-Abelian dual superconductivity picture for quark confinement, and demonstrated the numerical evidences on the lattice. In this talk, we focus on the the confinement and deconfinement phase transition at finite temperature in view of the dual superconductivity. By using our new formulation of lattice Yang-Mills theory and numerical simulations on the lattice, we extract the dominant mode for confinement by decomposing the Yang-Mills field, and we investigate the Polyakov loop av…
The abelian projection of lattice gluodynamics is reviewed. The main topics are: abelian and monopole dominance, monopole condensate as the disorder parameter, effective abelian Lagrangian, monopoles in the instanton field, Aharonov -- Bohm effect on the lattice.
We present results of $SU(3)$ Monte-Carlo studies of a new color confinement scheme due to Abelian-like monopoles of the Dirac type without any gauge-fixing. We get (1) perfect Abelian dominance with respect to the static potentials on $12^4\sim 16^4$ lattice at $β=5.6-5.8$ using the multilevel method, (2) monopole as well as Abelian dominances with respect to the static potentials by evaluating Polyakov loop correlators on $24^3\times4$ lattice at $β=5.6$. (3) Abelian dual Meissner effects are studied directly by measuring Abelian color fields and monopole currents around the static source. T…
If non-Abelian gauge fields in $SU(3)$ QCD have a line-singularity leading to non-commutativity with respect to successive partial-derivative operations, the non-Abelian Bianchi identity is violated. The violation as an operator is shown to be equivalent to violation of Abelian-like Bianchi identities. Then there appear eight Abelian-like conserved magnetic monopole currents of the Dirac type in $SU(3)$ QCD. Exact Abelian (but kinematical) symmetries appear in non-Abelian $SU(3)$ QCD. Here we try to show the Abelian dual Meissner effect due to the above Abelian-like monopoles are responsible f…
We study the relation between instantons and monopoles in the abelian gauge. First, we investigate the monopole in the multi-instanton solution in the continuum Yang-Mills theory using the Polyakov gauge. At a large instanton density, the monopole trajectory becomes highly complicated, which can be regarded as a signal of monopole condensation. Second, we study instantons and monopoles in the SU(2) lattice gauge theory both in the maximally abelian (MA) gauge and in the Polyakov gauge. Using the $16^3 \times 4$ lattice, we find monopole dominance for instantons in the confinement phase even at…
We have studied the monopole-percolation phenomenon in the four dimensional Abelian theory that contains compact U(1) gauge fields coupled to unitary norm Higgs fields. We have determined the location of the percolation transition line in the plane $(β_g, β_H)$. This line overlaps the confined-Coulomb and the confined-Higgs phase transition lines, originated by a monopole-condensation mechanism, but continues away from the end-point where this phase transition line stops. In addition, we have determined the critical exponents of the monopole percolation transition away from the phase transitio…
A new gauge (m-gauge) condition is proposed by means of a generalization of the Maximal Abelian gauge (MAG). The new gauge admits a space time dependent embedding of the residual U(1) into the SU(2) gauge group. This embedding is characterized by a color vector $\vec{m}(x)$. It turns out that this vector only depends of gauge invariant parts of the link configurations. Our numerical results show color ferromagnetic correlations of the $\vec{m}(x)$ field in space-time. The correlation length scales towards the continuum limit. For comparison with the MAG, we introduce a class of gauges which sm…
We present results of $SU(3)$ Monte-Carlo studies of a new color confinement scheme proposed recently due to Abelian-like monopoles of the Dirac type corresponding in the continuum limit to violation of the non-Abelian Bianchi identities (VNABI). The simulations are done without any additional gauge-fixing smoothing the vacuum. We get for the first time, in pure $SU(3)$ simulations with the standard Wilson action, (1) the perfect Abelian dominance with respect to the static potentials on $12^4\sim 16^4$ lattices at $β=5.6-5.8$ using the multilevel method. (2) The perfect monopole as well as Ab…
We study the Abelian projected SU(2) lattice gauge theory after gauge fixing to the maximally Abelian gauge (MAG). In order to check the universality of the Abelian dominance we employ the tadpole improved tree level (TI) action. We show that the density of monopoles in the largest cluster (the IR component) is finite in the continuum limit which is approximated already at relatively large lattice spacing. The value itself is smaller than in the case of Wilson action. We present results for the ratio of the Abelian to non-Abelian string tension for both Wilson and TI actions for a number of la…
We study the Abelian projection of SU(2) instantons in the Maximally Abelian gauge. We find that in this gauge an isolated instanton produces a closed monopole loop within its core and the size of this loop increases with the core size. We show that this result is robust against the introduction of small quantum fluctuations. We investigate the effects of neighbouring (anti)instantons upon each other and show how overlapping (anti)instantons can generate larger monopole loops. We find, however, that in fields that are typical of the fully quantised vacuum only some of the large monopole loops …
We study the properties of configurations from which P-vortices on one hand or Abelian monopoles on the other hand have been removed. We confirm the loss of confinement in both cases and investigate in what respect the modified ensembles differ from the confining ones from the point of view of the complementary confinement scenario.
Monopole and photon contributions to abelian Wilson loops are calculated using Monte-Carlo simulations of finite-temperature $SU(2)$ QCD in the maximally abelian gauge. Long monopole loops alone are responsible for the behavior of the string tension in the confinement phase up to the critical $β_c$. Short monopole loops and photons do not contribute to the string tension. The abelian and the monopole spacial string tensions (both of which agree with the normal ones for $β< β_c$) show a $g^{4}(T) T^2$ scaling behavior in the deconfinement phase. The abelian spacial string tension is in agreemen…
We study the density and spatial distribution of thermal Abelian monopoles in the deconfined phase of SU(2) pure gauge theory: they display non-trivial interactions with a well defined continuum limit. The Maximal Abelian Gauge (MAG) has been chosen to perform the Abelian projection. Questions related to the choice of the Abelian projection, as well as possible directions for future studies, are discussed.
Monte-Carlo simulations of abelian projection of $T \neq 0$ pure lattice QCD show that 1) Polyakov loops written in terms of abelian link fields alone play a role of an order parameter of deconfinement transition, 2) the abelian Polyakov loops are decomposed into contributions from Dirac strings of monopoles and from photons, 3) vanishing of the abelian Polyakov loops in the confinement phase is due to the Dirac strings alone and the photons give a finite contribution in both phases. Moreover, these results appear to hold good with any abelian projection as seen from the studies in the maximal…
Recently, we have developed a reformulation of the lattice Yang-Mills theory based on the change of variables a la Cho-Faddeev-Niemi combined with a non-Abelian Stokes theorem. In this talk, we give a new procedure (called reduction) for obtaining the color field which plays the central role in this reformulation. In the 4D SU(2) lattice Yang-Mills theory, we confirm the gauge-independent "abelian" dominance and gauge-independent magnetic-monopole dominance in the string tension extracted from the Wilson loop in the fundamental representation.
We have proposed the non-Abelian dual superconductivity in SU(3) Yang-Mills theory for the mechanism of quark confinement,and we presented the numerical evidences in preceding lattice conferences by using the proposed gauge link decomposition to extract magnetic monopole in the gauge invariant way. In this talk, we focus on the dual Meissner effects in view of the magnetic monopole in SU(3) Yang-Mills theory. We measure the chromoelectric and chromomagnetic flux due to a pair of quark and antiquark source at finite temperature. Then, we measure the correlation function of Polyakov loops and Po…
The dual Meissner effect is described and numerically observed in a gauge-invariant way in lattice Monte-Carlo simulations of pure SU(2) QCD. A gauge-invariant monopole-like quantity on the lattice is defined by a gauge-invariant Abelian-like field strength. The Abelian-like field strength is expressed in terms of a unit-vector in color space which is constructed by a non-Abelian field strength itself. It is just equal to the absolute value of the corresponding non-Abelian field strength except for the sign. In this note we show the theoretical background and most numerical results will be pub…
