Abelian-projected SU Research Articles

Detailed study of the Abelian-projected SU(2) flux tube and its dual Ginzburg-Landau analysis

The color-electric flux tube of Abelian-projected (AP) SU(2) lattice gauge theory in the maximally Abelian gauge (MAG) is examined. It is shown that the lattice Gribov copy effect in the MAG is crucial for the monopole-related parts of the flux-tube profiles. Taking into account both the gauge fixing procedure and the effect of finite quark-antiquark distance properly, the scaling property of the flux-tube profile is confirmed. The quantitative relation between the measured AP flux tube and the flux-tube solution of the U(1) dual Abelian Higgs (DAH) model is also discussed. The fitting of the AP flux tube in terms of the DAH flux tube indicates that the vacuum can be classified as a weakly type-I dual superconductor.

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.

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.

Effective string action for the U(1)×U(1) dual Ginzburg–Landau theory beyond the London limit

The effective string action of the color-electric flux tube in the U(1)×U(1) dual Ginzburg–Landau (DGL) theory is studied by performing a path-integral analysis by taking into account the finite thickness of the flux tube. The DGL theory, corresponding to the low-energy effective theory of Abelian-projected SU(3) gluodynamics, can be expressed as a [U(1)] 3 dual Abelian Higgs (DAH) model with a certain constraint in the Weyl symmetric formulation. This formulation allows us to adopt quite similar path-integral techniques as in the U(1) DAH model, and therefore, the resulting effective string action in the U(1)×U(1) DGL theory has also quite a similar structure except the number of color degrees of freedom. A modified Yukawa interaction appears as a boundary contribution, which is completely due to the finite thickness of the flux tube, and is reduced into the ordinary Yukawa interaction in the deep type-II (London) limit.

Dual formulation of gauge theories and confinement

We review various approaches to the problem of string representation of gauge theories allowing for the analytic description of confinement. The models under study include QCD within the stochastic vacuum model, compact QED, and Abelian-projected SU(2) theory.

A possible universal treatment of the field strength correlator in the Abelian-projected SU(2)-theory

An integral relation between two functions parametrizing the bilocal field strength correlator within the Stochastic Vacuum Model is obtained in the effective Abelian-projected SU(2)-theory. This relation is independent of the concrete properties of the ensemble of vortex loops, which are present in the theory under study. By virtue of the lattice result stating that the infrared asymptotic behaviours of these functions should have the same functional form, the obtained relation enables one to find these behaviours, as well as the infrared asymptotics of the bilocal correlator of densities of the vortex loops. Those turn out to be exponentials, decreasing at the inverse mass of the dual vector boson, times certain polynomials in the inverse integer powers of the distance. This result agrees with the general predictions and the existing lattice data better than the results of previous calculations, where these powers were found to be half-integer ones.

Topological and confining properties of Abelian-projected SU(3)-QCD

In this talk, we discuss several topics related to the Abelian-projected SU(3)-QCD. First of them is the Aharonov-Bohm effect emerging during the extension of this theory by the introduction of the Θ-term. Another topic is devoted to various consequences of screening of the dual vector bosons by electric vortex loops. In particular, it is demonstrated that this effect modifies significantly the magnetic part of interaction of quarks, which owing to the Θ-term acquire a nonvanishing magnetic charge. Next, the influence of screening to electric and magnetic field correlators in the four-dimensional Abelian-projected SU(3)-QCD is studied. Finally, the bilocal correlator of electric field strengths in the three-dimensional gas of SU(3) Abelian-projected monopoles is discussed.

Field correlators in Abelian-projected theories and stochastic vacuum model

The bilocal electric field strength correlators in Abelian-projected SU(2)- and SU(3)-theories are derived with accounting for the contributions to these quantities brought about by the virtual vortex loops, built out of the dual Nielsen-Olesen strings. Owing to the screening of magnetic charge of the dual vector bosons in the gas of such loops, these bosons become heavier, which leads to the respective change of the correlation length of the vacuum in the models under study. Besides that, it turns out that such a screening leads also to the appearance of the long-range contribution to one of the two coefficient functions, which parametrize the bilocal correlator within the Stochastic Vacuum Model. Finally, the modifications of the propagators of the dual vector bosons, inspired by the correlation effects in the gas of vortex loops, are also discussed.

Confining properties of Abelian-projected theories and field strength correlators

We review the string representations of Abelian-projected SU(2)- and SU(3)-gauge theories and their application to the evaluation of bilocal field strength correlators. The large distance asymptotic behaviours of the latter ones are shown to be in agreement with the Stochastic Vacuum Model of QCD and existing lattice data.

Vortex structure vs. monopole dominance in Abelian-projected gauge theory

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 structure. Further evidence is provided, in lattice Monte Carlo simulations, for collimation of confining color-magnetic flux into vortices.

Aharonov–Bohm effect in the Abelian-projected SU(3)-QCD with Θ-term

By making use of the path-integral duality transformation, string representation of the Abelian-projected SU(3)-QCD with the Θ-term is derived. Besides the short-range (self-)interactions of quarks (which due to the Θ-term acquire a nonvanishing magnetic charge, i.e. become dyons) and electric Abrikosov–Nielsen–Olesen strings, the resulting effective action contains also a long-range topological interaction of dyons with strings. This interaction, which has the form of the 4D Gauss linking number of the trajectory of a dyon with the world-sheet of a closed string, is shown to become nontrivial at Θ≠3π× integer . At these values of Θ, closed electric Abrikosov–Nielsen–Olesen strings in the model under study can be viewed as solenoids scattering dyons, which is the 4D analogue of the Aharonov–Bohm effect.

Confining properties of Abelian-projected theories

Representations of the Abelian-projected SU(2)- and SU(3)-gluodynamics in terms of the magnetic monopole currents are derived. Besides the quadratic part, the obtained effective actions contain interactions of these currents with the world-sheets of electric strings in 4D or electric vortex lines in 3D. Next, we illustrate that 3D compact QED is a small gauge boson mass limit of 3D Abelian Higgs model with external monopoles and give a physical interpretation to the confining string theory as the integral over the monopole densities. Finally, we derive the bilocal field strength correlator in the weak-field limit of 3D compact QED, which turns out to be in line with the one predicted by the Stochastic Vacuum Model.

On the perfect lattice actions of abelian-projected SU(2) QCD

We study the perfect lattice actions of abelian-projected SU(2) gluodynamics. Using the BKT and duality transformations on the lattice, an effective string model is derived from the direction-dependent quadratic monopole action, obtained numerically from SU(2) gluodynamics in maximally abelian gauge. The string tension and the restoration of continuum rotational invariance are investigated using strong coupling expansion of lattice string model analytically. We also found that the block spin transformation can be performed analytically for the quadratic monopole action.

Chiral symmetry breaking in Abelian-projected SU(2) lattice gauge theory.

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 ($\beta<1$) gauge theory: the chiral condensate is insensitive to $\beta$ and quark mass and hence violates scaling badly.