Search

New analysis regarding the structure of center vortices is presented: Using data from gluonic SU(2) lattice simulation with Wilson action, a correlation of fluctuations in color space to the curvature of vortex fluxes was found. Finite size effects of the S2-homogeneity hint at color homogeneous regions on the vortex surface.

In search for an effective model of quark confinement we study the vacuum of SU(2) quantum chromodynamic with lattice simulations using Wilson action. Assuming that center vortices are the relevant excitations causing confinement, we analyzed their physical size and their color structure. We present confirmations for a vanishing thickness of center vortices in the continuum limit and hints at their color structure. This is the first time that algorithms for the detection of thick center vortices based on non-trivial center regions has been used.

Gauge fields control the dynamics of fermions, also a back reaction of fermions on the gauge field is expected. This back reaction is investigated within the vortex picture of the QCD vacuum. We show that the center vortex model reproduces the string tension of the full theory also with the presence of fermionic fields., New data and new evaluations with different coaouthors. This version is submitted to MDPI / Universe

The center vortex model of quantum-chromodynamics can explain confinement and chiral symmetry breaking. We present a possible resolution for problems of the vortex detection in smooth configurations and discuss improvements for the detection of center vortices.

The center vortex model of quantum chromodynamic states that vortices, a closed color-magnetic flux, percolate the vacuum. Vortices are seen as the relevant excitations of the vacuum, causing confinement and dynamical chiral symmetry breaking. In an appropriate gauge, as direct maximal center gauge, vortices are detected by projecting onto the center degrees of freedom. Such gauges suffer from Gribov copy problems: different local maxima of the corresponding gauge functional can result in different predictions of the string tension. By using nontrivial center regions&mdash, that is, regions whose boundary evaluates to a nontrivial center element&mdash, a resolution of this issue seems possible. We use such nontrivial center regions to guide simulated annealing procedures, preventing an underestimation of the string tension in order to resolve the Gribov copy problem.

We discuss a model with stable topological solitons in Minkowski space with only three degrees of freedom, the rotational angles of a spatial Dreibein. This model has four types of solitons differing in two topological quantum numbers which we identify with electric charge and spin. The vacuum has a two-dimensional degeneracy leading to two types of massless excitations, characterised by a topological quantum number which could have a physical equivalent in the photon number., Comment: 9 pages

We investigate the chiral properties of near-zero modes for thick classical center vortices in SU (2) lattice gauge theory as examples of the phenomena which may arise in a vorex vacuum. In particular we analyze the creation of near-zero modes from would-be zero modes of various topological charge contributions from center vortices. We show that colorful spherical vortex and instanton ensembles have very similar Dirac eigenmodes and also vortex intersections are able to give rise to a finite density of near-zero modes, leading to chiral symmetry breaking via the Banks-Casher formula. We discuss the influence of the magnetic vortex fluxes on quarks and how center vortices may break chiral symmetry.

We investigate the chiral properties of near-zero modes for thick classical center vortices in SU(2) lattice gauge theory as examples of the phenomena which may arise in a vortex vacuum. In particular we analyze the creation of near-zero modes from would-be zero modes of various topological charge contributions from center vortices. We show that classical colorful spherical vortex and instanton ensembles have almost identical Dirac spectra and the low-lying eigenmodes from spherical vortices show all characteristic properties for chiral symmetry breaking. We further show that also vortex intersections are able to give rise to a finite density of near-zero modes, leading to chiral symmetry breaking via the Banks-Casher formula. We discuss the mechanism by which center vortex fluxes contribute to chiral symmetry breaking.

Within the effective quark model with chiral U (3) × U (3) symmetry we calculate the S-wave and P-wave amplitudes of the nonleptonic decay Σ+ → pπ0, the partial width and the dynamical polarization of the proton in the dependence on the polarization of the Σ+-hyperon. The theoretical results agree well with the experimental data.

We analyse the renormalizability of the sine-Gordon model using the two-point causal Green function. We show that all divergences can be removed by the renormalization of the dimensional coupling constant using the renormalization constant Z1, calculated in Faber and Ivanov (2003 J. Phys. A: Math. Gen. 36 7839) within the path-integral approach. We calculate the Gell-Mann–Low function and solve the Callan–Symanzik equation for the two-point Green function. We analyse the renormalizability of Gaussian fluctuations around a soliton. We show that Gaussian fluctuations around a soliton solution are renormalized like quantum fluctuations around the trivial vacuum and do not introduce any singularity to the sine-Gordon model at β2 = 8π. We calculate the correction to the soliton mass, caused by Gaussian fluctuations around a soliton, within the discretization procedure for various boundary conditions and find complete agreement with our result, obtained in continuous space–time.

We investigate the influence of the granularity of the lattice on the potential between monopoles. Using the flux definition of monopoles we introduce their centers of mass and are able to realize continuous shifts of the monopole positions. We find periodic deviations from the $1/r$-behavior of the monopole-antimonopole potential leading to local extrema. We suppose that these meta-stabilities may influence the order of the phase transition in compact QED., Comment: 11 pages, 5 figures

We investigate the chiral properties of near-zero modes for thick classical center vortices in $SU(2)$ lattice gauge theory as examples of the phenomena which may arise in a vortex vacuum. In particular we analyze the creation of near-zero modes from would-be zero modes of various topological charge contributions from center vortices. We show that classical colorful spherical vortex and instanton ensembles have almost identical Dirac spectra and the low-lying eigenmodes from spherical vortices show all characteristic properties for chiral symmetry breaking. We further show that also vortex intersections are able to give rise to a finite density of near-zero modes, leading to chiral symmetry breaking via the Banks-Casher formula. We discuss the mechanism by which center vortex fluxes contribute to chiral symmetry breaking.

The Nambu–Jona–Lasinio model of the deuteron suggested by Nambu and Jona–Lasinio (Phys. Rev. 124 (1961) 246) is formulated from the first principles of QCD. The deuteron appears as a neutron–proton collective excitation, i.e. a Cooper np–pair, induced by a phenomenological local four–nucleon interaction in the nuclear phase of QCD. The model describes the deuteron coupled to itself, nucleons and other particles through one–nucleon loop exchanges providing a minimal transfer of nucleon flavours from initial to final nuclear states and accounting for contributions of nucleon–loop anomalies which are completely determined by one–nucleon loop diagrams. The dominance of contributions of nucleon–loop anomalies to effective Lagrangians of low–energy nuclear interactions is justified in the large NC expansion, where NC is the number of quark colours.

Interquark confinement potential is calculated in the dual Monopole Nambu-Jona-Lasinio model with dual Dirac strings as a functional of a dual Dirac string length. The calculation is carried out by the explicit integration over quantum fluctuations of a dual-vector field (monopole-antimonopole collective excitation) around the Abrikosov flux line and string shape fluctuations. The contribution of the scalar field (monopole-antimonopole collective excitation) exchange is taken into account in the tree approximation due to the London limit regime., 10 pages, Latex, no figures

The magnetic monopole condensate is calculated in the dual Monopole Nambu-Jona-Lasinio model with dual Dirac strings suggested in Refs.[1,2] as a functional of the dual Dirac string shape. The calculation is carried out in the tree approximation in the scalar monopole-antimonopole collective excitation field. The integration over quantum fluctuations of the dual-vector monopole-antimonopole collective excitation field around the Abrikosov flux line and string shape fluctuations are performed explicitly. We claim that there are important contributions of quantum and string shape fluctuations to the magnetic monopole condensate., Comment: 19 pages, Latex, 2 figures

We propose a model of monopoles where a condensate of monopole-antimonopole pairs leads to confinement. We investigate the condensation of these monopole-antimonopole pairs around a dual Dirac string.

We investigate the polarization cloud around static electric charges in the framework of compact lattice QED. We calculate the correlations of Polyakov loops with the electric charge densityψ†ψ normalized to the chiral condensate. It turns out that virtual anticharges screen static charges as expected from continuum QED. Charge polarization is more pronounced at strong couplings and extends to a longer range on the lattice in the weak coupling phase. In both phases the correlations decrease with larger fermion mass.

We suggest a relativistic field theory model of the deuteron. We start from a local unphysical deuteron field, taken as a bound proton-neutron state at zero binding energy. Following the Nambu-Jona-Lasinio prescription we construct the physical deuteron field. We describe all parameters of the physical deuteron in the one-nucleon loop approximation and in leading order of the long-wavelength expansion. The one-pion exchange contribution to the binding energy calculated in the two-nucleon loop approximation is found small compared with that obtained in the one-nucleon loop one. The present model can be applied to the description of the decouplet of dibaryons 10 f where the deuteron is the component with Y = 2 and I = 0.

Chiral symmetry breaking is explored within QCD with linearly rising confinement potential at the Nambu-Jona-Lasinio (NJL) prescription. The dynamical quark mass is obtained from the gap equation in terms of the string tension σ, σ,i.e.m=2蜰σ/π=0.33 GeV at σ=0.27 GeV2. The phenomenological constants of the NJL local four-quark interactionsG1 andG2 are found equal and expressed in terms of the string tension and the confinement radius. It is shown that the spectra of low-lying quark-antiquark collective excitations coincide with those predicted by the NJL model.

We use the Bethe-Salpeter equation for the investigation of the mass spectra of four nonets of low-lying mesons (pseudoscalar, scalar, vector and axial-vector) within QCD with a linearly rising potential. In leading order in the large- N expansion and in the chiral limit the mass spectra are found in agreement with those predicted by the extended Nambu-Jona-Lasinio model. We show that due to the confinement potential the nonets of vector and axial-vector mesons are stable under decays into quark-antiquark pairs.

The vacuum structure of QCD in an external chromo-electric field is investigated within the continuum space-time formulation of perturbative QCD and the extended NambuJona-Lasinio model, used as a low-energy approximation of QCD. We show that the density of dynamical quark-antiquark pairs decreases with increasing external chromoelectric field strength. These results are compared with recent numerical simulations of lattice QCD which indicate restoration of chiral symmetry in the vicinity of a static color

We investigate the QCD vacuum structure around static quarks and mesons by calculating the correlation of Polyakov loops with the local chiral condensate ψψ( r ) . We find that the restoration of chiral symmetry in the vicinity of static color sources increases with decreasing bare mass of virtual quarks.

We analyze the vacuum structure of compact lattice QED affected by static electric sources. The potential and the energy density between a static charge and anticharge are computed. Potentials are screened by dynamical fermions and energy distributions are localized around the sources. We further compute the electric charge density ψ † ψ and find that static charges are screend by virtual anticharges as expected from ordinary QED. All effects are more pronounced at strong coupling and decrease with growing fermion mass.

For the low-energy approximation of QCD, the extended Nambu-Jona-Lasinio model has been used. Quarks interact with an external homogeneous color-magnetic field, simulating the contribution of the gluon condensate. The value of the gluon condensate, needed to reach the correct value of the quark condensate, is determined and agrees well with the value obtained from QCD sum rules.

We study the origin of the Coulomb part of the quark-antiquark potential by lattice calculations. A cooling technique which reduces quantum noise in lattice configurations is applied. We demonstrate that the Coulomb part of the potential vanishes with cooling and is thus due to quantum fluctuations, while the string tension persists many cooling steps. Further, we give an estimate of the energy contained in quantum fluctuations.

The vacuum structure of QCD with dynamical fermions around a static quark-antiquark pair is explored by calculating the correlation functions L ( r 1 ) L † ( r 2 ) O ( r )> between a static meson and several characteristic observables for which we choose the chiral condensate, the charge density, and the energy density. We find a restoration of chiral symmetry around static color sources as a consequence of gluon string creation and a screening of static quarks by virtual antiquarks in analogy to QED. Our computations explicitly exhibit the formation of a chromoelectric flux tube and its breaking in the presence of dynamical quarks.

We investigate the QCD vacuum structure around static hadrons by calculating the correlations of Polyakov loops with the local chiral condensate ψ ψ( r ) and the color charge density ψ † ψ( r ) . We find that chiral symmetry is restored in the vicinity of static color sources as a consequence of gluon string creation and that virtual antiquarks screen static quarks in analogy to QED.

We analyze the model of topological fermions (MTF), where charged fermions are treated as soliton solutions of the field equations. In the region far from the sources we find plane waves solutions with the properties of electro-magnetic waves., 4 pages, 2 figures

The dually transformed path integral of four-dimensional U(1) lattice gauge theory is used for a numerical investigation of multiply charged systems and the interaction between flux tubes. For this aim, it is convenient to implement periodically closed flux tubes (torelons) in the dual formulation. We calculate the free energy as well as the total electro-magnetic energy of doubly charged flux tubes as a function of the coupling β. The main results are that the string tension scales proportionally to the charge (contrary to the Coulomb potential) and in the range 0.9

We consider pure gluonic SU (3) lattice gauge theory and determine colour magnetic currents by measuring the total magnetic flux out of unit lattice cubes. To study the influence of these currents on physical quantities we modify the Wilson action and add an extra term suppressing the currents. We present first results of numerical simulations which show that a suppression of magnetic currents strongly influences the string tension and the critical coupling for the finite temperature phase transition.

In the model of low-energy bar-K N interactions near threshold (EPJA 21, 11 (2004); 25, 79 (2005)) we calculate isospin-breaking corrections to the energy level displacement of the ground state of kaonic hydrogen, investigated by Meissner, Raha and Rusetsky (EPJC 35, 349 (2004)) within the non-relativistic effective Lagrangian approach based on ChPT by Gasser and Leutwyler. Our results agree well with those by Mei��ner et al.. In addition we calculate the dispersive corrections, caused by the transition K^-p -> bar-K^0n ->K^-p with the bar-K^0n pair on-mass shell. We show also how hypothesis on the dominant role of the bar-K^0n-cusp for the S-wave amplitude of low-energy K^-p scattering near threshold, used by Meissner et al., can be realized in our approach. The result agrees fully with that by Meissner et al.., Latex, 24 pages, 1 figure, the manuscript is revised

We consider a model of topological solitons where charged particles have finite mass and the electric charge is quantised already at the classical level. In the electrodynamic limit, which physically corresponds to electrodynamics of solitons of zero size, the Lagrangian of this model has two degrees of freedom only and reduces to the Lagrangian of the Maxwell field in dual representation. We derive the equations of motion and discuss their relations with Maxwell's equations. It is shown that Coulomb and Lorentz forces are a consequence of topology. Further, we relate the U(1) gauge invariance of electrodynamics to the geometry of the soliton field, give a general relation for the derivation of the soliton field from the field strength tensor in electrodynamics and use this relation to express homogeneous electric fields in terms of the soliton field., Comment: 13 pages, 4 figures, Introduction and Section II (Model Lagrangian) rewritten, new chapters concerning electrodynamic limit and discussion of causality inserted

The confinement in compact QED is known to be related to magnetic monopoles. Magnetic currents form a solenoid around electric flux lines between a pair of electric charges. This behaviour can be described by the dual version of Maxwell—London equations including a fluctuating string. We use a definition of magnetic monopole currents adjusted to the definition of the electric field strength on a lattice and get good agreement for field and current distributions between compact QED and the predictions of dual Maxwell—London equations. Further we show that the monopole fluctuations in the vacuum are suppressed by the flux tube.

We consider pionic hydrogen A_(pi p), the bound pi^- p state. Within the quantum field theoretic and relativistic covariant approach we calculate the shift and width of the energy level of the ground state of pionic hydrogen caused by strong low-energy interactions treated perturbatively. The generalization of the Deser-Goldberger-Baumann-Thirring (DGBT) formulas (Phys. Rev. 96, 774 (1954)) is given. The generalized DGBT formulas for the energy level displacement of the ground state of pionic hydrogen contain the non-perturbative and model-independent correction about 1%, caused by the relativistic covariant smearing of the wave function of the ground state around origin. This non-perturbative correction is very important for the precise extraction of the S-wave scattering lengths of pion-nucleon scattering from the experimental data on the energy level displacements in pionic hydrogen by the PSI Collaboration. In addition the shift of the energy level of the ground state of pionic hydrogen is improved by the second order correction of strong low-energy interactions which is about 0.1%. This testifies the applicability of the perturbative treatment of strong low-energy interactions to the analysis of pionic hydrogen. We show that the width of the energy level of the ground state of pionic hydrogen is valid to all order of perturbation theory in strong low-energy interactions., 24 pages, latex, no figures, corrected according to the version accepted for publication in EPJA

We study the SU(2) gauge-Higgs system in D=4 dimensions, and analyze the influence of the fundamental-representation Higgs field on the vortex content of the gauge field. It is shown that center projected Polyakov lines, at low temperature, are finite in the infinite volume limit, which means that the center vortex distribution is consistent with color screening. In addition we confirm and further investigate the presence of a "Kertesz-line" in the strong-coupling region of the phase diagram, which we relate to the percolation properties of center vortices. It is shown that this Kertesz-line separates the gauge-Higgs phase diagram into two regions: a confinement-like region, in which center vortices percolate, and a Higgs region, in which they do not. The free energy of the gauge-Higgs system, however, is analytic across the Kertesz line., Comment: 7 pages, 10 figures

The charge density around a static charge is investigated within finite temperature QCD and compact QED both in the chirally broken and symmetric phase. We display the functional behavior of the charge polarization for various masses of the sea particles and for static sources in higher representations. The total induced charge is found to be consistent with the results from the MILC Collaboration.

The charge density around a static charge is investigated within finite temperature QCD and compact QED both in the chirally broken and symmetric phase. We analyze the functional behavior of the charge polarization and compare it to a weak coupling estimate. The total induced charge is found to be consistent with the results of the MILC Collaboration.

We review lattice evidence for the vortex mechanism of quark confinement and study the influence of charged matter fields on the vortex distribution., Comment: 10 pages, 6 eps figures, talk presented by M.F. at the 5th International Conference "Quark Confinement and the Hadron Spectrum", Gargnano, Italy, September 10-14, 2002

We develop an analytical approach for non-abelian gauge models within the plaquette representation where the plaquette matrices play the role of the fundamental degrees of freedom. We start from the original Batrouni formulation and show how it can be modified in such a way that each non-abelian Bianchi identity contains two connectors instead of four. Using this representation we construct the low-temperature expansion for U (1) and SU (N) models on a finite lattice and discuss its uniformity in the volume. Next, we derive a dual representation for the 't Hooft loop in the SU (2) model and describe monopoles in the maximal axial gauge.

We present a variety of numerical data supporting the Center Vortex theory of confinement. A method is introduced for identifying the location of center vortices, in thermalized gauge-field configurations generated by lattice Monte Carlo. Fluctuations in the number of such vortices, linked to fundamental representation Wilson loops, appear to be responsible for the asymptotic string tension extracted from those loops., Comment: Invited talk by J. Greensite at the Nato Workshop "New Developments in Quantum Field Theory," Zakopane, Poland (June 1997). 19 pages, including 21 figures, Latex2e. Uses plenum.sty

The D-wave state component of the neutron-proton bound state in the deuteron is calculated in the Nambu-Jona-Lasinio model of light nuclei - the relativistically covariant quantum field theoretic approach to the description of low-energy nuclear forces. The theoretical value of the fraction of the D-wave state relative to the S-wave state is equal to eta_d = 0.0238. This agrees well with the phenomenological value eta_d = 0.0256(4) quoted by Kamionkowski and Bahcall (ApJ. 420, 884 (1994))., 7 pages, latex, no figures

Studying potentials between quark multiplets at finite temperature we find that at large distances all potentials become either screened or have the same string tension as the 3 - 3 potential. Thus, in the confining phase the string tension between different color sources depends only on triality zero or nonzero. The underlying mechanism is a screening of sources by virtual gluons either completely (e.g. octet sources) or partially (e.g. sextet sources) so that either singlet or triplet charges remain. Concerning the Coulomb part and the constant term of the potentials we achieve good agreement for the ratios of different multiplets with a Casimir scaling law already at β = 5.6.

A model for the infrared sector of SU(2) Yang-Mills theory, based on magnetic vortices represented by (closed) random surfaces, is presented. The random surfaces, governed by an action penalizing curvature, are investigated using Monte Carlo methods on a hypercubic lattice. A low-temperature confining phase and a high-temperature deconfined phase are generated by this simple dynamics. After fixing the parameters of the model such as to reproduce the relation between deconfinement temperature and zero-temperature string tension found in lattice Yang-Mills theory, a surprisingly accurate prediction of the spatial string tension in the deconfined phase results. Furthermore, the Pontryagin index associated with the lattice random surfaces of the model is constructed. This allows to also predict the topological susceptibility; the result is compatible with measurements in lattice Yang-Mills theory. Thus, for the first time an effective model description of the infrared sector emerges which simultaneously and consistently reproduces both confinement and the topological aspects of Yang-Mills theory within a unified framework. Further details can be found in hep-lat/9912003 and hep-lat/0004013, both to appear in Nucl. Phys. B., 12 latex pages, 4 epsf figures; talk presented by M.Engelhardt at the Fourth Workshop on "Continuous Advances in QCD", Minneapolis, 12.-14.5.2000, to appear in the proceedings

Abelian gauge theories formulated on a space-time lattice can be used as a prototype for investigating the confinement mechanism. In U(1) lattice gauge theory it is possible to perform a dual transformation of the path integral. Simulating the obtained dual theory (which corresponds to a certain limit of a dual Higgs model) including external sources, we perform a very accurate analysis of flux tubes with respect to the dual superconductor picture. Dual flux tube simulations are also performed in the full Abelian Higgs model, in order to obtain non-perturbative control over quantum and string fluctuations, and for a comparison to the results of dual QCD.

Here we report on some investigations of the phase structure of hot gauge theories defined in the canonical ensemble (CE) [1]-[3]. Usually, the deconfinement phase transition is associated with the appearence of nonzero triality in the hot phase [4, 5]. In particular Z(N) gauge theories with Higgs fields have been precisely analyzed [5]. Since it was known that at zero temperature these systems have two phases, a confining/screening phase and a deconfining one [6] separated by a critical line and since such a critical line was not found it has been concluded that at finite T the critical behaviour may not be present at all. However, it is not obvious a priori that “free triality states” indeed exist in the deconfined phase. There might be a phase transition unrelated to the triality liberation but rather to different screening mechanisms of triality. We present some results which indicate that this can be the case. The idea is to generalize a certain A operator introduced in [7] to finite T theory and to study its behaviour in the CE.

We discuss the implementation of the ``direct'' maximal center gauge (a gauge which maximizes the lattice average of the squared-modulus of the trace of link variables), and its use in identifying Z(2) center vortices in Yang-Mills vacuum configurations generated by lattice Monte Carlo. We find that center vortices identified in the vacuum state account for the full asymptotic string tension. Scaling of vortex densities with lattice coupling, change in vortex size with cooling, and sensitivity to Gribov copies is discussed. Preliminary evidence is presented, on small lattices, for center dominance in SU(3) lattice gauge theory., 28 pages including 18 figures, Latex2e

We report on two recent developments in the center vortex theory of confinement: (i) the asymptotic scaling of the vortex density, as measured in Monte Carlo simulations; and (ii) an explanation of Casimir scaling and the adjoint string tension, in terms of the center vortex mechanism., Comment: LATTICE98(confine), 3 pages, 3 figures

We modify the standard Wilson action of SU(3) lattice gauge theory by adding an extra term which suppresses colour magnetic currents. We present numerical results of simulations at zero and finite temperature and show that colour magnetic currents strongly influence the confining properties of SU(3) lattice gauge theory., 11 pages, latex, 8 pslatex-figures included, complete postscript file also available at ftp://is1.kph.tuwien.ac.at/pub/skala/pl97.ps.gz, to be published in Phys. Lett. B, replaced to match version accepted for publication

The S-wave scattering length of the strong pion-deuteron (pi D) scattering is calculated in the relativistic field theory model of the deuteron suggested in [1,2].The theoretical result agrees well with the experimental data. The important role of the Delta-resonance contribution to the elastic pi D-scattering is confirmed., 7 pages, no figures, accepted for publication in Z. Phys. A