Abelian Wilson Loop Research Articles

Monopoles of the Dirac type and color confinement in QCD: First results of SU(3) numerical simulations without gauge fixing

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 for color confinement in $SU(3)$ QCD. If this picture is correct, the string tension of non-Abelian Wilson loops is reproduced fully by that of the Abelian Wilson loops. This is called as perfect Abelian dominance. In this report, the perfect Abelian dominance is shown to exist with the help of the multilevel method but without introducing additional smoothing techniques like partial gauge fixings, although lattice sizes studied are not large enough to study the infinite volume limit. Perfect monopole dominance is also shown without any additional gauge fixing. Abelian electric fields are squeezed due to solenoidal monopole currents and the penetration length for an Abelian electric field of a single color is the same as that of non-Abelian electric field. The coherence length is also measured directly through the correlation of the monopole density and the Polyakov loop pair. The Ginzburg-Landau parameter indicates that the vacuum type is the weak type I (dual) superconductor. The results obtained above without any additional assumptions as well as more clear previous $SU(2)$ results seem to suggest strongly the above Abelian dual Meissner picture of color confinement mechanism.

Abelian Fock - Schwinger representation for the quark propagator in external gauge field

We develop the Diakonov - Petrov approach to the representation of the non - Abelian Wilson loop in an Abelian form. First of all, we extend this approach to the Abelian representation of the parallel transporter corresponding to the open curve rather than to the closed contour. Next, we extend this representation to the case of the non - compact groups. The obtained expressions allow us to derive the Abelian form of the Schwinger - Fock representation for the quark propagator in an external color gauge field.

Intersection of world-lines on curved surfaces and path-ordering of the Wilson loop

We study contact interactions for long world-lines on a curved surface, focusing on the average number of times two world-lines intersect as a function of their end-points. The result can be used to extend the concept of path-ordering, as employed in the Wilson loop, from a closed curve into the interior of a surface spanning the curve. Taking this surface as a string world-sheet yields a generalisation of the string contact interaction previously used to represent the Abelian Wilson loop as a tensionless string. We also describe a supersymmetric generalisation.

Duality of gauge field singularities and the structure of the flux tube in Abelian-projected SU(2) gauge theory and the dual Abelian Higgs model

The structure of the flux-tube profile in Abelian-projected (AP) SU(2) gauge theory in the maximally Abelian gauge is studied. The connection between the AP flux tube and the classical flux-tube solution of the U(1) dual Abelian Higgs model is clarified in terms of the path-integral duality transformation. This connection suggests that the electric photon and the magnetic monopole parts of the Abelian Wilson loop can act as separate sources creating the Coulombic and the solenoidal electric field inside a flux tube. The conjecture is confirmed by a lattice simulation which shows that the AP flux tube is composed of these two contributions.

Abelian Duality and Abelian Wilson Loops

We consider a pure U(1) quantum gauge field theory on a general Riemannian compact four manifold. We compute the partition function with Abelian Wilson loop insertions. We find its duality covariance properties and derive topological selection rules. Finally, we show that, to have manifest duality, one must assume the existence of twisted topological sectors besides the standard untwisted one.

A fresh look at the flux tube in Abelian-projected SU(2) gluodynamics

We reconsider the properties of the QQ¯ flux tube within Abelian-projected SU(2) lattice gauge theory in terms of electric field and monopole current. In maximal Abelian gauge fixing, we assess the influence of Gribov copies on the apparent flux-tube profile. For the profile corresponding to optimal gauge fixing, we study the independence of the lattice spacing for β = 2.3, 2.4, and 2.5115 on a 32 4 lattice. We apply the decomposition of the Abelian Wilson loop into monopole and photon parts and compare the electric and monopole profile emerging from these three different sources with the field strength and monopole current within the DGL theory.

Gauge problem of monopole dynamics inSU(2)lattice gauge theory

Gauge problem of monopole dynamics is studied in SU(2) lattice gauge theory. We study first abelian and monopole contributions to the static potential in four smooth gauges, i.e., Laplacian Abelian (LA), Maximally Abelian Wilson Loop (MAWL) and L-type gauges in comparison with Maximally Abelian (MA) gauge. They all reproduce the string tension in good agreement with the SU(2) string tension. MA gauge is not the only choice of the good gauge which is suitable for the color confinement mechanism. Using an inverse Monte-Carlo method and the blockspin transformation, we determine effective monopole actions and the renormalization group (RG) flows of its coupling constants in various abelian projection schemes. Every RG flow looks to converge to a unique curve which suggests gauge independence in the infrared region.

Abelian dominance and adjoint sources in lattice QCD.

Certain properties of maximal abelian projection are derived which suggest that the fundamental and adjoint SU(2) string tensions are reproduced by singly and doubly charged abelian Wilson loops, respectively. Thus, abelian dominance, which has been observed for color sources (quarks) in the fundamental representation, can be extended to higher representations. Numerical evidence in support of this conjecture also for adjoint quarks is presented. The difference between maximal abelian and local projections is elucidated and the role of non-Wilson-like terms in the effective abelian action is discussed.

String tension and monopoles in T ≠ 0 SU(2) QCD

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. The string tension is reproduced by monopole contribution alone also in finite temperature SU(2) QCD. The spatial string tension scales as $\sqrt{\sigma} \propto g^{2}(T)T$ and is reproduced almost by monopole contribution alone. Each configuration has one long monopole loop, and the long monopole loops alone are responsible for the string tension in the confinement phase. On the other hand, the spatial string tension in the deconfinement phase is reproduced by wrapped monopole loops alone.

String tension and monopoles in T ≠ 0 SU(2) QCD

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. Short monopole loops and photons do not contribute to the string tension. The abelian and the monopole spatial string tensions (both of which agree with the full ones for β< β c ) show a g 4( T) T 2 scaling behavior in the deconfinement phase. The abelian spatial string tension is in agreement with the full one even in the deconfinement phase.

Monopoles and string tension in SU(2) QCD

Monopole and photon contributions to abelian Wilson loops are calculated using Monte Carlo simulations of SU(2) QCD in the maximally abelian gauge. The string tension is well reproduced only by monopole contributions, whereas photons alone are responsible for the Coulomb coefficient of the abelian static potential.

The (dual) Meissner effect in SU(2) and SU(3) QCD

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.

Can monopoles alone reproduce the string tension also in SU(2) lattice QCD?

We study if monopoles alone can reproduce the string tension in SU (2) QCD. The situations in SU (2) QCD are not so simple as those in compact QED. We follow the procedure in the t'Hooft-Polyakov monopole case and separate the monopole contributions from abelian Wilson loops in the maximally abelian gauge. Preliminary data show that they seem reproduce the string tension.

3D SU(2) pure gauge theory in the maximally abelian gauge

We investigate SU(2)3 lattice gauge theory in 3 Euclidean dimensions using maximally abelian gauge. We show that abelian monopole density is constant in continuum limit. The Creutz ratios produced from abelian Wilson loops are close to ordinary Creutz ratios. We find evident correlations between Creutz ratios and monopole density.

Abelian projection of QCD and Abelian Wilson loops

Performing numerical simulations and abelian projection in SU(2) QCD, we find abelian Wilson loops composed of a residual U(1) gauge field alone show clear area-law behaviors with small Coulomb effects in a U(1) covariant gauge. There is an indication of abelian dominance in quark confinement. Nonrenormalizable unitary gauges do not show such interesting behaviors.

Possible evidence for Abelian dominance in quark confinement.

Performing numerical simulations and Abelian projection in SU(2) QCD, we find that Wilson loops composed of a residual U(1) gauge field alone show a strong enhancement when the Abelian projection is done in a U(1)-covariant gauge. Remarkably, the Creutz ratios determined from the Abelian Wilson loops approach the scaling curve with $\sqrt{\ensuremath{\sigma}}\ensuremath{\sim}58{\ensuremath{\Lambda}}_{L}$. Nonrenormalizable unitary gauges do not show such interesting types of behavior.

Green functions of vortex operators

We study the euclidean Green functions of the 't Hooft vortex operator, primarily for abelian gauge theories. The operator is written in terms of elementary fields, with emphasis on a form in which it appears as the exponential of a surface integral. We explore the requirement that the Green functions depend only on the boundary of this surface. The Dirac veto problem appears in a new guise. We present a two-dimensional “solvable model” of a Dirac string, which suggests a new solution of the veto problem. The renormalization of the Green functions of the abelian Wilson loop and abelian vortex operator is studied with the aid of the operator product expansion. In each case, an overall multiplication of the operator makes all Green functions finite; a surprising cancellation of divergences occurs with the vortex operator. We present a brief discussion of the relation between the nature of the vacuum and the cluster properties of the Green functions of the Wilson and vortex operators, for a general gauge theory. The surface-like cluster property of the vortex operator in an abelian Higgs theory is explored in more detail.