Decomposition of SU(2) gauge field into the monopole and monopoleless components is studied in the Maximal Abelian gauge using Monte-Carlo simulations in lattice SU(2) gluodynamics as well as in two-color QCD with both zero and nonzero quark chemical potential. The interaction potential between static charges is calculated for each component and their sum is compared with the non-Abelian static potential. A good agreement is found in the confinement phase. Implications of this result are discussed.
We show that the instantons induce the abelian monopoles in the Maximal Abelian Projection of $SU(2)$ gluodynamics. As an example we consider the case of one instanton and the case of a set of instantons arranged along a straight line. The abelian monopoles which are induced by instantons may play some role in the confinement scenario.
We calculate the Faddeev-Popov operator corresponding to the maximally Abelian gauge for gauge group SU(N). Specializing to SU(2) we look for explicit zero modes of this operator. Within an illuminating toy model (Yang-Mills mechanics) the problem can be completely solved and understood. In the field theory case we are able to find an analytic expression for a normalizable zero mode in the background of a single `t Hooft instanton. Accordingly, such an instanton corresponds to a horizon configuration in the maximally Abelian gauge. Possible physical implications are discussed.
We present an algorithm for simulation of $SU(2)$ lattice gauge theory under the MA gauge and first numerical results for the theory without abelian monopoles. The results support the idea that nonperturbative interaction arises between monopoles and residual abelian field and the other interactions are perturbative. It is shown that the Gribov region for the theory with the MA gauge fixed is non-connected.
On lattice gauge field configurations with 2+1 dynamical quark flavors, we investigate the momentum space quark and gluon propagators in the combined maximally Abelian plus $U(1)_3\times U(1)_8$ Landau gauge. We extract the gluon fields from the lattice link variables and study the diagonal and off-diagonal gluon propagators. We find that the infrared region of the transverse diagonal gluon propagator is strongly enhanced compared to the off-diagonal propagator. The Dirac operator from the Asqtad action is inverted on the diagonal and off-diagonal gluon backgrounds separately. In agreement wit…
We investigate the dual superconductor hypothesis in finite-temperature SU(2) lattice gluodynamics in the Spatial Maximal Abelian gauge. This gauge is more physical than the ordinary Maximal Abelian gauge due to absence of non-localities in temporal direction. We show numerically that in the Spatial Maximal Abelian gauge the probability distribution of the abelian monopole field is consistent with the dual superconductor mechanism of confinement: the abelian condensate vanishes in the deconfinement phase and is not zero in the confinement phase.
We study abelian dominance for confinement in terms of the local gluon properties in the maximally abelian (MA) gauge in a semi-analytical manner with the help of the lattice QCD. The global Weyl symmetry persistently remains as the relic of SU($N_c$) in the MA gauge, and provides the ambiguity on the electric and magnetic charges. We derive the criterion on the SU($N_c$)-gauge invariance in terms of the residual symmetry in the abelian gauge. In the lattice QCD, we find microscopic abelian dominance on the link variable for the whole region of $β$ in the MA gauge. The off-diagonal angle varia…
We calculate the static quark potential for an SU(N) gauge theory in the Maximal Abelian gauge as well as its Abelian projection up to two loops in perturbation theory. We discuss its renormalization properties. The result is compared with a recent lattice result at $r \lesssim 0.5$ fm.
Correlations of the topological charge Q, the electric current J^e and the magnetic current J^m in SU(2) lattice gauge theory in the Maximal Abelian projection are investigated. It occurs that the correlator <<QJ^e J^m>> is nonzero for a wide range of values of the bare charge. It is shown that: (i) the abelian monopoles in the Maximal Abelian projection are dyons which carry fluctuating electric charge; (ii) the sign of the electric charge e(x) coincides with that of the product of the monopole charge m(x) and the topological charge density Q(x).
We derive the Schwinger-Dyson equations for the SU(2) Yang-Mills theory in the maximal Abelian gauge and solve them in the infrared asymptotic region. We find that the infrared asymptotic solutions for the gluon and ghost propagators are consistent with the hypothesis of Abelian dominance.
Propagators of diagonal and off-diagonal gluons are studied numerically in the Maximally Abelian gauge of the SU(2) lattice gauge theory. We have found the strong enhancement of the diagonal gluon in the infrared region. The enhancement factor is about 50 at the smallest available momentum, 325 MeV. We discuss also various analytical fits to the propagators.
We present results for the fundamental string tension in SU(2) lattice gauge theory after projection to maximal abelian and direct maximal center gauges. We generate 20 Gribov copies/configuration. Abelian and center projected string tensions slowly decrease as higher values of the gauge functionals are reached.
Propagators of the diagonal and the off-diagonal gluons are studied numerically in the Maximal Abelian gauge of SU(2) lattice gauge theory. It is found that in the infrared region the propagator of the diagonal gluon is strongly enhanced in comparison with the off--diagonal one. The enhancement factor is about 50 at our smallest momentum 325 MeV. We have also applied various fits to the propagator formfactors.
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 discuss and propose a proper extension of the Abelian projection based on the Maximal Abelian Gauge to SU(N) gauge theories. Based, on that, we investigate the properties of thermal Abelian monopoles in the deconfined phase of the SU(3) pure gauge theory. Such properties are very similar to those already found for SU(2), confirming the relevance of the magnetic component close to Tc and the possible condensation of thermal monopoles as the deconfinement temperature is crossed from above. Moreover, we study the correlation functions among monopoles related to different U(1) subgroups, which …
The construction outlined by Henyey is employed to provide examples of normalizable zero modes of the Faddeev-Popov operator in the Landau and maximal Abelian gauges in SU(2) Euclidean Yang-Mills theories in d=3 dimensions. The corresponding gauge configurations have all finite norm ||A||^2 < \infty. In particular, in the case of the Landau gauge, the explicit construction of an infinite class of normalizable zero modes with finite norm ||A||^2 is provided.
Various field strength correlators are investigated in the maximal abelian projection of pure SU(2) lattice gauge theory. High precision measurements of the colour fields, monopole currents, their curl and divergence allow for detailed checks of the dual superconductor scenario. A further decomposition of abelian observables into monopole and photon parts reveals that the flux tube is built up from the monopole part alone.
We introduce a generalized Maximum Abelian Gauge (MAG). We work with this new gauge on 12^4 lattices for beta=5.7,5.8 and 16^4 lattices for beta=5.9,6.0. We also introduce a form of abelian projection related to the generalized MAG. We measure U(1)xU(1) wilson loops and single color magnetic current densities.
We apply smoothing to SU(2) lattice field configurations in 3+1 dimensions before fixing to the maximally Abelian gauge. The Abelian projected string tension is shown to be stable under this, whilst the monopole string tension declines by O(30%). Blocking of the SU(2) fields reduces this effect, but the use of extended monopole definitions does not. We discuss these results in the context of additional confining excitations in the U(1) vacuum.
The infrared behavior of the gluon and ghost propagators is studied in SU(2) Euclidean Yang-Mills theory in the maximal Abelian gauge within the Gribov-Zwanziger framework. The nonperturbative effects associated with the Gribov copies and with the dimension two condensates are simultaneously encoded into a local and renormalizable Lagrangian. The resulting behavior turns out to be in good agreement with the lattice data.
The confinement scenario in Maximally Abelian gauge (MAG) is based on the concepts of Abelian dominance and of dual superconductivity. Recently, several groups pointed out the possible existence in MAG of ghost and gluon condensates with mass dimension 2, which in turn should influence the infrared behavior of ghost and gluon propagators. We present preliminary results for the first lattice numerical study of the ghost propagator and of ghost condensation for pure SU(2) theory in the MAG.
A qualitative study of the lightest glueball states in Euclidean SU(2) Yang-Mills theory quantized in the maximal Abelian gauge is presented. The analysis is done by generalizing to the maximal Abelian gauge the so-called replica model, already successfully introduced in the Landau gauge. As it will be shown, the gluon and ghost propagators obtained from the replica model are of the same type of those already introduced in Phys. Rev. D77, 105023 (2008) [arXiv:0801.0566], whose behavior turns out to be in agreement with that available from the lattice data on the maximal Abelian gauge. The mode…
We show that the monopole confinement mechanism in lattice gluodynamics is a particular feature of the maximal abelian projection. We give an explicit example of the $SU(2) \rightarrow U(1)$ projection (the minimal abelian projection), in which the confinement is due to topological objects other than monopoles. We perform analytical and numerical study of the loop expansion of the Faddeev--Popov determinant for the maximal and the minimal abelian projections, and discuss the fundamental modular region for these projections.
We study the properties of gluons in QCD in the maximally abelian (MA) gauge. In the MA gauge, the off-diagonal gluon behaves as the massive vector boson with the mass $\Meff \simeq 1.2 {\rm GeV}$, and therefore the off-diagonal gluon cannot carry the long-range interaction for $r \gg \Meff^{-1} \simeq 0.2$ fm. The essence of the infrared abelian dominance in the MA gauge is physically explained with the generation of the off-diagonal gluon mass $\Meff \simeq 1.2 {\rm GeV}$ induced by the MA gauge fixing, and the off-diagonal gluon mass generation would predict general infrared abelian dominan…
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 study the gluon propagator in the MA gauge with the lattice QCD Monte Carlo simulation. The simulation is performed using the heat-bath algorithm on the SU(2) lattice with $12^3 \times 24$ and $β= 2.3, 2.35$. The propagator of the off-diagonal charged gluon behaves as the massive gauge boson and provides the short-range interaction, while the diagonal gluon propagates long distance. This is the origin of the abelian dominance in the long-range physics.
The effects of the Gribov copies on the gluon and ghost propagators are investigated in SU(2) Euclidean Yang-Mills theory quantized in the maximal Abelian gauge. The diagonal component of the gluon propagator displays the characteristic Gribov type behavior. The off-diagonal component of the gluon propagator is found to be of the Yukawa type, with a dynamical mass originating from the dimension two condensate <A^2>, which is also taken into account. Finally, the off-diagonal ghost propagator exhibits infrared enhancement.
The study of Yang-Mills theories in three dimensions is an insightful playground to grasp important features for the four-dimensional case. Additionally, in three dimensions, the Chern-Simons term can be introduced with a mass parameter of topological nature. Quantizing such a theory in the continuum demands a gauge fixing which, in general, is plagued by Gribov copies. In this work, Yang-Mills-Chern-Simons theories are quantized in the maximal Abelian gauge and the existence of infinitesimal Gribov copies is taken into account. The elimination of copies modifies the (Abelian) gluon propagator…
We study propagators of diagonal and off-diagonal gluons in the momentum space in maximal abelian gauge of SU(2) lattice gauge theory. Remaining U(1) degrees of freedom are fixed using Landau gauge. We find substantial difference between the propagator of the diagonal and the off-diagonal gluon in the infrared region. The propagator of the off-diagonal gluon is suppressed in comparison with that of the diagonal gluon at small momenta. In the ultraviolet region both propagators behave as in nonabelian Landau gauge.
We gauge fix 600 SU(3) beta=6.0 configurations on a 16^4 lattice to a simple form of the maximal abelian gauge. We project the SU(3) valued links to the U(1)xU(1) subgroup, and extract U(1)xU(1) and monopole string tensions. After gauge fixing to the indirect center gauge, the U(1)xU(1) links are projected to Z(3) and a vortex string tension is measured. The vortex and magnetic current densities are measured.
Various field strength correlators are investigated in the maximal Abelian projection of pure SU(2) lattice gauge theory. High precision measurements of the colour fields, monopole currents, their curls and divergences allow for detailed checks of the dual superconductor scenario. On this basis, we perform a Ginzburg-Landau type analysis of the flux tube profile from which we derive the size of the penetration length, LAMBDA = 0.16(2) fm, and coherence length of the monopole condensate wave function, XI = 0.27(3) fm. The ratio of these numbers is KAPPA = LAMBDA/XI = 0.59(13) which is below the…
An improved method for extracting infrared exponents from functional equations is presented. The generalizations introduced allow for an analysis of quite complicated systems such as Yang-Mills theory in the maximally Abelian gauge. Assuming the absence of cancellations in the appropriately renormalized integrals the only consistent scaling solution yields an infrared enhanced diagonal gluon propagator in support of the Abelian dominance hypothesis. This is explicitly shown for SU(2) and subsequently verified for SU(N), where additional interactions exist. We also derive the most infrared dive…
We construct the local Gribov-Zwanziger action for SU(2) Euclidean Yang-Mills theories in the maximally Abelian (MA) gauge with U(1)$_3$ Landau gauge fixing based on the Zwanziger's work in the Landau gauge. By the restriction of the functional integral region to the Gribov region in the MA gauge, we give the nonlocal action. We localize the action with new fields and obtain the action with the shift of the new scalar fields, which has the terms, corresponding to the localized action of the horizon function in the MA gauge. The diagonal gluon propagator in the MA gauge at tree level behaves li…
The general problem of obtaining reliable results from gauge-fixing and projection is discussed. It is shown that the usual form of the maximal abelian gauge gives poor results for the string tension in SU(3) lattice gauge theory. A generalized form is suggested. Evidence is presented that monopoles in SU(3) are associated with SU(2) subgroups, and that P-vortices pass through monopoles, similar to what happens in SU(2).
We show that off-diagonal gluons and off-diagonal ghosts acquire their masses dynamically in QCD if the maximal Abelian gauge is adopted. This result strongly supports the Abelian dominance in low-energy region of QCD. The mass generation is shown to occur due to ghost-anti-ghost condensation caused by attractive quartic ghost interactions within the Abelian projected effective gauge theory (derived by one of the authors). In fact, the quartic ghost interaction is indispensable for the renormalizability due to nonlinearity of the maximal Abelian gauge. The ghost-anti-ghost condensation is asso…
We investigate the Maximally Abelian (MA) Projection for a single $SU(2)$ instanton in continuum gauge theory. We find that there is a class of solutions to the differential MA gauge condition with circular monopole loops of radius $R$ centered on the instanton of width $ρ$. However, the MA gauge fixing functional $G$ decreases monotonically as $R/ρ\rightarrow 0$. Its global minimum is the instanton in the singular gauge. We point out that interactions with nearby anti-instantons are likely to excite these monopole loops.
Perturbative approach to the infrared gluon propagator in the maximal Abelian gauge
ICTP South American Institute for Fundamental Research（ICTP南美基础研究所）；Instituto de Física Teórica, UNESP - Univ. Estadual Paulista（UNESP圣保罗州立大学理论物理研究所）；EEEFM Agenor de Souza Lé（EEEFM阿格诺尔·德索萨·莱学院）；Instituto de Física, Universidade Federal Fluminense（弗鲁米嫩塞联邦大学物理研究所）；Universidade do Estado do Rio de Janeiro, Instituto de Física –Departamento de Física Teórica（里约热内卢州立大学物理系理论物理研究所）
We study decomposition of $SU(2)$ gauge field into monopole and monopoleless components. After fixing the Maximal Abelian gauge in $SU(2)$ lattice gauge theory we decompose the nonabelian gauge field into the Abelian field created by monopoles and the modified nonabelian field with monopoles removed. We then calculate respective static potentialis and show that the potential due to the modified nonabelian field is nonconfining while, as is well known, the Abelian field produces linear potential. We further find that the sum of these potentials approximates the nonabelian static potential with …
We investigate a dynamical mass generation mechanism for the off-diagonal gluons and ghosts in SU(N) Yang-Mills theories, quantized in the maximal Abelian gauge. Such a mass can be seen as evidence for the Abelian dominance in that gauge. It originates from the condensation of a mixed gluon-ghost operator of mass dimension two, which lowers the vacuum energy. We construct an effective potential for this operator by a combined use of the local composite operators technique with the algebraic renormalization and we discuss the gauge parameter independence of the results. We also show that it is …
We study effective mass generation of off-diagonal gluons and infrared abelian dominance in the maximally abelian (MA) gauge. Using the SU(2) lattice QCD, we investigate the propagator and the effective mass of the gluon field in the MA gauge with the U(1)$_3$ Landau gauge fixing. The Monte Carlo simulation is performed on the $12^3 \times 24$ lattice with $2.2 \le β\le 2.4$, and also on the $16^4$ and $20^4$ lattices with $2.3 \le β\le 2.4$. In the MA gauge, the diagonal gluon component $A_μ^3$ shows long-range propagation, and infrared abelian dominance is found for the gluon propagator. In …
We pursue the study of SU(2) Euclidean Yang-Mills theory in the maximal Abelian gauge by taking into account the effects of the Gribov horizon. The Gribov approximation, previously introduced in [1], is improved through the introduction of the horizon function, which is constructed under the requirements of localizability and renormalizability. By following Zwanziger's treatment of the horizon function in the Landau gauge, we prove that, when cast in local form, the horizon term of the maximal Abelian gauge leads to a quantized theory which enjoys multiplicative renormalizability, a feature wh…
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 …
In this report, I discuss lattice Monte Carlo evidence of excitations of isolated static charges in q=2 Abelian Higgs theory. The localized excitations are excited states of the interacting fields surrounding the static charges.
In this work, we study the propagators of matter fields within the framework of the Refined Gribov-Zwanziger theory, which takes into account the effects of the Gribov copies in the gauge-fixing quantization procedure of Yang-Mills theory. In full analogy with the pure gluon sector of the Refined Gribov-Zwanziger action, a non-local long-range term in the inverse of the Faddeev-Popov operator is added in the matter sector. Making use of the recent BRST invariant formulation of the Gribov-Zwanziger framework achieved in [Capri et al 2016], the propagators of scalar and quark fields in the adjoi…
We discuss some properties of abelian monopoles in the Maximal Abelian projection of the SU(2) lattice gluodynamics. We show that in the maximal abelian projection abelian monopoles carry fluctuating electric charge and that the monopole currents are correlated with the magnetic and the electric parts of the SU(2) action density.
Chiral symmetry breaking parameters are calculated in quenched SU(2) gauge theory and with Abelian gauge fields projected in maximal Abelian gauge and in field strength gauge. Maximal Abelian gauge projected fields lead to chiral condensate values which are quite similar to those of the full nonabelian theory. Pseudoscalar and vector meson correlators are calculated and found to be reproduced by the use of maximal Abelian gauge fields for small quark masses. In field-strength gauge, Abelian-projected fields give a chiral condensate which closely resembles the results of strongly coupled ($β<1$…
We study the Nambu-'t Hooft picture for color confinement in terms of the abelianization of QCD and monopole condensation in the maximally abelian (MA) gauge. In the MA gauge in the Euclidean metric, the off-diagonal gluon amplitude is strongly suppressed, and then the off-diagonal gluon phase shows strong randomness, which leads to rapid reduction of the off-diagonal gluon correlation. In SU(2) and SU(3) lattice QCD in the MA gauge with the abelian Landau gauge, the Euclidean gluon propagator indicates a large effective mass of the off-diagonal gluon as $M_{\rm off} \simeq 1 {\rm GeV}$ in the…
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…
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 report on calculations of the heavy quark potential in SU(3) lattice gauge theory. Full SU(3) results are compared to three cases which involve gauge-fixing and projection. All of these start from the maximal abelian gauge (MAG), in its simplest form. The first case is abelian projection to U(1)xU(1). The second keeps only the abelian fields of monopoles in the MAG. The third involves an additional gauge-fixing to the indirect maximal center gauge (IMCG), followed by center projection to Z(3). At one gauge fixing/configuration, the string tensions calculated from MAG U(1)xU(1), MAG monopole…
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 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…
We study abelianization of QCD in the maximally abelian (MA) gauge. In the MA gauge, the off-diagonal gluon amplitude is strongly suppressed, and then the off-diagonal gluon phase shows strong randomness, which leads to a large off-diagonal gluon mass. Using lattice QCD, we find a large effective off-diagonal gluon mass in the MA gauge: $M_{\rm off} \simeq 1.2 {\rm GeV}$ in SU(2) QCD, $M_{\rm off} \simeq 1.1 {\rm GeV}$ in SU(3) QCD. Due to the large off-diagonal gluon mass in the MA gauge, infrared QCD is well abelianized like nonabelian Higgs theories. We investigate the inter-monopole potent…
The one loop 3-point vertex functions of QCD in the maximal abelian gauge (MAG) are evaluated at the fully symmetric point at one loop. As a consequence the theory is renormalized in the various momentum (MOM) schemes which are defined by the trivalent vertices, as well as in the MSbar scheme. From these the two loop renormalization group functions in the MOM schemes are derived using the one loop conversion functions. In parallel we repeat the analysis for the Curci-Ferrari gauge which corresponds to the MAG in a specific limit. The relation between the Lambda parameters in different schemes …
Dual formulations of Abelian U(1) and Z(N) LGT with a static fermion determinant are constructed at finite temperatures and non-zero chemical potential. The dual form is valid for a broad class of lattice gauge actions, for arbitrary number of fermion flavors and in any dimension. The distinguished feature of the dual formulation is that the dual Boltzmann weight is strictly positive. This allows to gain reliable results at finite density via the Monte Carlo simulations. As a byproduct of the dual representation we outline an exact solution for the partition function of the (1 + 1)-dimensional…
We present lattice Monte Carlo evidence of stable excitations of isolated static charges in the Higgs phase of the charge $q=2$ abelian Higgs model. These localized excitations are excited states of the interacting fields surrounding the static charges. Since the $q=2$ abelian Higgs model is a relativistic version of the Landau-Ginzburg effective action of a superconductor, we conjecture that excited states of this kind might be relevant in a condensed matter context. Taken together with recent related work in SU(3) gauge Higgs theory, our result suggests that a massive fermion excitation spec…
We formulate a stochastic gauge fixing method to study the gauge dependence of the Abelian projection. We consider a gauge which interpolates between the maximal Abelian gauge and no gauge fixing. We have found that Abelian dominance for the heavy quark potential holds even in a gauge which is far from maximally Abelian one. The heavy quark potentials from monopole and photon contribution are calculated at several values of the gauge parameter, and the former part shows always the confinement behavior.
In SU(3) lattice QCD formalism, we propose a method to extract gauge fields from link-variables analytically. With this method, we perform the first study on effective mass generation of off-diagonal gluons and infrared Abelian dominance in the maximally Abelian (MA) gauge in the SU(3) case. Using SU(3) lattice QCD, we investigate the propagator and the effective mass of the gluon fields in the MA gauge with U(1)$_3 \timesU(1)_8$ Landau gauge fixing. The Monte Carlo simulation is performed on $16^4$ at $β$=5.7, 5.8 and 6.0 at the quenched level. The off-diagonal gluons behave as massive vector…
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…
