We continue our investigation of quark confinement using a particular variant of the Cho-Duan-Ge gauge independent Abelian decomposition. The decomposition splits the gauge field into a restricted Abelian part and a coloured part in a way that preserves gauge covariance. The restricted part of the gauge field can be divided into a Maxwell term and a topological term. Previously, we showed that by a particular choice of this decomposition we could fully describe the confining potential using only the restricted gauge field. We proposed that various topological objects (a form of magnetic monopole) could arise in the restricted field which would drive confinement. Our mechanism does not explicitly refer to a dual Meissner effect, nor does it use centre vortices. We did not need to gauge fix or introduce any new dynamical fields.
We show that if we do gauge fix as well as performing the Abelian decomposition then it is possible to ensure that the topological part of the restricted field fully accounts for the confining potential. Our relationship is exact: there is no approximation or model involved. This isolates the objects responsible for confinement from non-confining contributions to the gauge field, allowing a direct search for our proposed topological objects. Using numerical studies in SU(2), we confirm that our proposed monopoles are present in the field, and the winding number associated with these monopoles is a key factor driving quark confinement.
In SU(2), our monopoles are described by two parameters. We show that it is possible to re-parametrise the Yang Mills action and the functional integration measure in terms of these variables (plus the necessary additional parameters). We can thus treat the monopoles as dynamical variables in the functional integral. This might be the first step in a future analytical computation to complement our numerical results.
A projection (gauge) independent formulation of the monopole dominance, discovered in lattice QCD for the maximal abelian projection, is given. A new dynamical abelian projection of continuum QCD, which does not rely on any explicit gauge condition imposed on gauge fields, is proposed. Under the assumption that the results of numerical simulations holds in the continuum limit, the monopole dominance is proved for the dynamical abelian projection. The latter enables us to develop an effective scalar field theory for dominant (monopole) configurations of gauge fields. The approach is manifestly …
We describe a new order parameter for the confinement-deconfinement transition in lattice SU(2) Yang-Mills theory. It is expressed in terms of magnetic monopole field correlators represented as sums over sheets of center vortices. Our construction establishes a link between "abelian" and "center dominance". It avoids an inconsistency in the treatment of small scales present in earlier definitions of monopole fields by respecting Dirac's quantization condition for magnetic fluxes.
We find that Polyakov lines, computed in abelian-projected SU(2) lattice gauge theory in the confined phase, have finite expectation values for lines corresponding to two units of the abelian electric charge. This means that the abelian-projected lattice has at most Z(2), rather than U(1), global symmetry. We also find a severe breakdown of the monopole dominance approximation, as well as positivity, in this charge-2 case. These results imply that the abelian-projected lattice is not adequately represented by a monopole Coulomb gas; the data is, however, consistent with a center vortex structu…
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.
We show that the non-Abelian magnetic monopole defined in a gauge-invariant way in SU(3) Yang-Mills theory gives a dominant contribution to confinement of the fundamental quark, in sharp contrast to the SU(2) case.
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.
To check the dual superconductor picture for the quark-confinement mechanism, we evaluate monopole dominance as well as Abelian dominance of quark confinement for both quark-antiquark and three-quark systems in SU(3) quenched lattice QCD in the maximally Abelian (MA) gauge. First, we examine Abelian dominance for the static $Q\bar Q$ system in lattice QCD with various spacing $a$ at $β$=5.8-6.4 and various size $L^3$x$L_t$. For large physical-volume lattices with $La \ge$ 2fm, we find perfect Abelian dominance of the string tension for the $Q\bar Q$ systems: $σ_{Abel} \simeq σ$. Second, we acc…
We prove Abelian magnetic monopole dominance in the string tension of QCD. Abelian and monopole dominance in low energy physics of QCD has been confirmed for various quantities by recent Monte Carlo simulations of lattice gauge theory. In order to prove this dominance, we use the reformulation of continuum Yang-Mills theory in the maximal Abelian gauge as a deformation of a topological field theory of magnetic monopoles, which was proposed in the previous article by the author. This reformulation provides an efficient way for incorporating the magnetic monopole configuration as a topological n…
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 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 conde…
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…
We show that the QCD vacuum (without dynamical quarks) is a dual superconductor at least in the low-energy region in the sense that monopole condensation does really occur. In fact, we derive the dual Ginzburg-Landau theory (i.e., dual Abelian Higgs model) directly from the SU(2) Yang-Mills theory by adopting the maximal Abelian gauge. The dual superconductor can be on the border between type II and type I, excluding the London limit. The masses of the dual Abelian gauge field is expressed by the Yang-Mills gauge coupling constant and the mass of the off-diagonal gluon of the original Yang-Mil…
New topological objects, which we call center monopoles, naturally arise in the Maximal Center Projection of SU(3) gluodynamics. The condensate of the center monopoles is the order parameter of the theory.
The dual superconductor picture is one of the most promising scenarios for quark confinement. To investigate this picture in a gauge-invariant manner, we have proposed a new formulation of Yang-Mills theory, named the decomposition method, on the lattice. The so-called restricted field obtained from the gauge-covariant decomposition plays the dominant role in quark confinement. It has been known by preceding works that the restricted-field dominance is not observed for the Wilson loop in higher representations if the restricted part of the Wilson loop is obtained by adopting the Abelian projec…
In earlier work, we used a gauge independent Abelian Decomposition to show that Abelian degrees of freedom are wholly responsible for the static quark potential. The restricted Abelian field can be split into two terms, a Maxwell term and a $θ$ (Dirac) term. The $θ$ term's contribution to the string tension can be analysed theoretically and numerically, and arises because of the existence of a certain type of monopole. While the Abelian field can be constructed without gauge fixing, its two component parts are gauge-dependent, with a gauge transformation moving the topological features from on…
We analyze previously proposed order parameters for the confinement - deconfinement transition in lattice SU(2) Yang-Mills theory, defined as vacuum expectation value (v.e.v.) of monopole fields in abelian projection gauges. We show that they exhibit some inconsistency in the treatment of small scales, due to a violation of Dirac quantization condition for fluxes. We propose a new order parameter avoiding this inconsistency. It can be interpreted as v.e.v. of the field of a regular monopole in any abelian projection gauge, but it is independent of the choice of the abelian projection. Furtherm…
Numerical data for the SU(2) confining string in the maximal abelian projection are analysed. The distribution of the electric flux and monopole currents are perfectly described by the classical equations of motion for the dual Abelian Higgs model. The mass of the vector boson is equal to the mass of the monopole (Higgs particle) within numerical errors. The classical energy per unit length of the Abrikosov vortex reproduces 94% of the full non-Abelian string tension.
In most Yang-Mills models the vacuum where magnetic monopoles condense coincides with that where center vortices percolate, thus it is not clear which of these two properties is most directly involved in producing confinement. It is pointed out that there is a class of 3D gauge models, which can be though of as duals of Q-state Potts models with Q < 1, where the magnetic monopole condensation is a necessary but not sufficient condition for percolation of center vortices. A set of numerical tests at Q=1/10 shows that there is a vacuum in which the magnetic monopole condensate does not yield con…
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…
It is proven that dual superconductivity of QCD vacuum in the confining phase is an intinsic property, independent on the choice of the abelian projection used to define the monopoles.
Assuming the monopole dominance, that has been proved in the lattice gluodynamics, to hold in the continuum limit, we develop an effective scalar field theory for QCD at large distances to describe confinement. The approach is based on a gauge (or projection) independent formulation of the monopole dominance and manifestly Lorentz invariant.
We review the recent results in the physics of the magnetic monopoles in gluodynamics and a dual formulation of non-Abelian theories, relevant to the physics of the confinement. It occurs that the dual gluon is a U(1) gauge boson, despite of the fact that usual gluons are non-Abelian. The effective infrared Lagrangian for gluodynamics is suggested which leads to the Casimir scaling of the string tension for quarks in various representations. We also show that the results of the calculations in lattice gauge theories confirm our theoretical predictions.
The role of monopoles in the confining behavior of compact lattice $QED_3$ is studied using an adiabatic cooling method. Monopole-antimonopole pairs with large separation suvive cooling and the presence or absence of such plasma monopoles provides a useful classification of the lattice gauge field configurations at large $β$. By calculating observables in subsets of gauge field configurations which contain or do not contain plasma monopoles it is seen that, in compact $QED_3$, monopoles dominate the long distance physics, e.g., the string tension, linear confining potential and dynamical mass …
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…
We investigate the confining properties of the QCD vacuum with $N_f=2$ flavors of dynamical quarks, and compare the results with the properties of the quenched theory. We use non-perturbatively $\mathcal{O}(a)$ improved Wilson fermions to keep cut-off effects small. We focus on color magnetic monopoles. Among the quantities we study are the monopole density and the monopole screening length, the static potential and the profile of the color electric flux tube. We furthermore derive the low-energy effective monopole action. Marked differences between the quenched and dynamical vacuum are found.
We show that a certain type of color magnetic condensation originating from magnetic monopole configurations is sufficient to provide the mass for off-diagonal gluons in the SU(2) Yang-Mills theory under the Cho--Faddeev--Niemi decomposition. We point out that the generated gluon mass can cure the instability of the Savvidy vacuum. In fact, such a novel type of magnetic condensation is shown to occur by calculating the effective potential. This enables us to explain the infrared Abelian dominance and monopole dominance by way of a non-Abelian Stokes theorem, which suggests the dual superconduc…
Calculations of the chiral condensate on the lattice using staggered fermions and the Lanczos algorithm are presented. Four gauge fields are considered: the quenched non-Abelian field, an Abelian projected field, and monopole and photon fields further decomposed from the Abelian field. Abelian projection is performed in maximal Abelian gauge and in Polyakov gauge. The results show that monopoles in maximal Abelian gauge largely reproduce the chiral condensate values of the full non-Abelian theory, in both SU(2) and SU(3) color.
We study the topological feature in the QCD vacuum based on the hypothesis of abelian dominance. The topological charge $Q_{\rm SU(2)}$ can be explicitly represented in terms of the monopole current in the abelian dominated system. To appreciate its justification, we directly measure the corresponding topological charge $Q_{\rm Mono}$, which is reconstructed only from the monopole current and the abelian component of gauge fields, by using the Monte Carlo simulation on SU(2) lattice. We find that there exists a one-to-one correspondence between $Q_{\rm SU(2)}$ and $Q_{\rm Mono}$ in the maximal…
Confinement of electrically charged test particles in the dilute plasma of monopoles and pointlike magnetic dipoles is studied. We calculate the tension of the string emerging between the infinitely separated test particles. The string tension is an increasing function of the dipole density provided other parameters of the plasma are fixed. The relevance of our results to confining gauge theories is discussed.
Calculations of the chiral condensate $\langle \barψ ψ\rangle$ on the lattice using staggered fermions and the Lanczos algorithm are presented. Three gauge fields are considered: the quenched non-Abelian field, the Abelian field projected in the maximal Abelian gauge, and the monopole field further decomposed from the Abelian field. The results show that the Abelian monopoles largely reproduce the chiral condensate values of the full non-Abelian theory, both in SU(2) and in SU(3).
We review recent results from lattice on topological aspects of QCD: most of the results refer to monopoles and to instantons. We discuss in detail the evidence for condensation of monopoles in the vacuum and confinement of colour by dual superconductivity, and the major role of monopoles in dynamics (monopole dominance). As for instantons we review the $U(1)$ problem, a possible determination of the spin content of the proton, and new lattice data relevant to instanton liquid models.
We study spontaneous chiral-symmetry breaking in SU(3) QCD in terms of the dual superconductor picture for quark confinement in the maximally Abelian (MA) gauge, using lattice QCD Monte Carlo simulations with four different lattices of $16^4$, $24^4$, $24^3\times 6$ at $β=6.0$ (i.e., the spacing $a \simeq$ 0.1 fm), and $32^4$ at $β=6.2$ (i.e., $a \simeq$ 0.075 fm), at the quenched level. First, in the confinement phase, we find Abelian dominance and monopole dominance in the MA gauge for the chiral condensate in the chiral limit,using the two different methods of i) the Banks-Casher relation w…
The monopole order parameter of QCD is computed in terms of gauge invariant field strength correlators. Both quantities are partially known from numerical simulations on the lattice. A new insight results on the structure of the confining vacuum.
We address the question of defining the second quantised monopole creation operator in the 3+1 dimensional Georgi-Glashow model, and calculating its expectation value in the confining phase. Our calculation is performed directly in the continuum theory within the framework of perturbation theory. We find that, although it is possible to define the "coherent state" operator M(x) that creates the Coulomb magnetic field, the dependence of this operator on the Dirac string does not disappear even in the nonabelian theory. This is due to the presence of the charged fields (W^{\pm}). We also set up …
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…
We introduce quantum gauge fixing (QGF) as a new class of gauge fixings. While the maximal center gauge might not show vortex dominance, the confining properties of the vortices observed in past lattice calculations are argued to have been obtained in a gauge more akin to QGF than to the strict maximal center gauge.
We show the construction of the dual superconducting theory for the confinement mechanism from QCD in the maximally abelian (MA) gauge using the lattice QCD Monte Carlo simulation. We find that essence of infrared abelian dominance is naturally understood with the off-diagonal gluon mass $m_{\rm off} \simeq 1.2 {\rm GeV}$ induced by the MA gauge fixing. In the MA gauge, the off-diagonal gluon amplitude is forced to be small, and the off-diagonal gluon phase tends to be random. As the mathematical origin of abelian dominance for confinement, we demonstrate that the strong randomness of the off-…
We study infrared abelian dominance and the dual Higgs mechanism in the maximally abelian (MA) gauge using the lattice QCD Monte Carlo simulation. In the MA gauge, the off-diagonal gluon phase tends to be random, and the off-diagonal gluon $A_μ^\pm$ acquires the effective mass as $M_{\rm off} \simeq$ 1.2 GeV. From the monopole current in the MA gauge, we extract the dual gluon field $B_μ$ and estimate the dual gluon mass as $m_B \simeq $ 0.5 GeV. The QCD-monopole structure is also investigated in terms of off-diagonal gluons. From the lattice QCD in the MA gauge, the dual Ginzburg-Landau (DGL)…
We discuss predictions for the interaction energy of the fundamental monopoles in gluodynamics introduced via the 't Hooft loop. At short distances, the heavy monopole potential is calculable from first principles. At larger distances, we apply the Abelian dominance models. We discuss the measurements which would be crucial to distinguish between various models. Non-zero temperatures are also considered. Our predictions are in qualitative agreement with the existing lattice data. We discuss further measurements which would be crucial to check the model.
We show that the hypothesis of abelian dominance allows QCD-monopoles to preserve the topological feature of the QCD vacuum within SU(2) lattice gauge theory. An analytical study is made to find the relationship between the topological charge and QCD-monopoles in the lattice formulation. The topological charge is explicitly represented in terms of the monopole current and the abelian component of gauge fields in the abelian dominated system. We numerically examine the relation and demonstrate the abelian dominance in the topological structure by using Monte Carlo simulation.
We demonstrate that the disorder parameter $<μ>$ to detect dual superconductivity in the confining phase of QCD is the v.e.v. of a magnetically charged, Dirac like, gauge invariant operator $μ$. We also show that the abelian projection on the lattice is determined up to terms O(a^2) (a = lattice spacing).
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 instanton…
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…
Three topics concerning infrared effective lattice QCD are discussed. (1)Perfect lattice action of infrared SU(3) QCD and perfect operators for the static potential are analytically given when we assume two-point monopole interactions alone. The assumption seems to be justified from numerical analyses of pure SU(3) QCD in maximally abelian gauge. (2)Gauge invariance of monopole dominance can be proved theoretically if the gauge invariance of abelian dominance is proved. The gauge invariance of monopole condensation leads us to confinement of abelian neutral but color octet states after abelian…
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…
Finite temperature compact electrodynamics in (2+1) dimensions is studied in the presence of external electromagnetic fields. The deconfinement temperature is found to be insensitive to the external fields. This result corroborates our observation that external fields create additional small--size magnetic dipoles from the vacuum which do not spoil the confining properties of the model at low temperature. However, the Polyakov loop is not an order parameter of confinement. It can vanish in deconfinement in the presence of external field. This does not mean the restoration of confinement for ce…
Quark confinement is proposed to be a dual Meissner effect of nonAbelian kind. Important hints come from physics of strongly-coupled infrared-fixed-point theories in N=2 supersymmetric QCD, which turn into confining vacua under a small relevant perturbation. The quest for the semiclassical origin of the nonAbelian monopoles, ubiquitous as the infrared degrees of freedom in supersymmetric gauge theories, motivates us to study the quantum dynamics of 2D CP(N-1)model defined on a finite-width worldstrip, with various boundary conditions. The model is found to possess a unique phase ("confinement …
We present selected recent results of the QCDSF collaboration on the localization and dimensionality of low overlap eigenmodes and of the topological density in the quenched SU(3) vacuum. We discuss the correlations between the topological structure revealed by overlap fermions without filtering and the confining monopole and P-vortex structure obtained in the Indirect Maximal Center Gauge.
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 confining and topological properties of the compact Abelian Higgs model with doubly-charged Higgs field in three space-time dimensions are studied. We consider the London limit of the model. We show that the monopoles are forming chain-like structures (kept together by ANO vortices) the presence of which is essential for getting simultaneously permanent confinement of singly-charged particles and breaking of the string spanned between doubly-charged particles. In the confinement phase the chains are forming percolating clusters while in the deconfinement (Higgs) phase the chains are of fin…
We review some recent developments on BPS string solutions and monopole confinement in the Higgs or (color) superconducting phase of deformed N=2 and N=4 super Yang-Mills theories. In particular, the monopole magnetic fluxes are shown to be always integer linear combinations of string fluxes. Moreover, a bound for the threshold length of the string breaking is obtained. When the gauge group SU(N) is broken to Z_N, the BPS string tension satisfies the Casimir scaling law. Furthermore in the SU(3) case the string solutions are such that they allow the formation of a confining system with three m…
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…
The dual superconductivity is believed to be a promising mechanism for quark confinement. Indeed, what this picture is true has been confirmed in the maximal Abelian (MA) gauge. However, it is not yet confirmed in any other gauge and the MA gauge explicitly breaks color symmetry. To remedy this defect, we propose to use our compact formulation of a non-linear change of variables on a lattice. This formulation has succeeded to extract the magnetic monopole with integer-valued magnetic charge in the gauge-invariant way. In this talk, we present measurements of various correlation functions for t…
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.
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 subgrou…
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 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…
