Wolfgang Sakuler

Exact zero modes of the compact QED Dirac operator

Abstract We calculate the low-lying eigenmodes of the Neuberger overlap-Dirac operator for 4d compact lattice QED in the quenched approximation. In the strong coupling phase we find exact zero-modes, quite similar as in non-Abelian lattice QCD. Subsequently we make an attempt to identify responsible topological excitations of the U(1) lattice gauge theory.

Chiral symmetry and charge density in mesons for Kogut-Susskind and Wilson fermions

Abstract We investigate the sea quark distribution around static quarks in the framework of lattice QCD by calculating the correlations of Polyakov loops with the local chiral condensate ψ ψ(r) and the color charge density ψ † ψ(r) . A comparison of dynamical quarks in Kogut-Susskind and Wilson discretization is performed. We observe a restoration of chiral symmetry in the vicinity of color sources for both fermion regularization schemes as a consequence of gluon string formation. It turns out that virtual antiquarks screen static quarks as expected from QED.

Baryon-baryon potentials on the lattice☆

Abstract The interaction of spatially extended heavy baryons is investigated in the framework of lattice QCD with dynamical quarks. It is shown that the expected dipole forces have a very short range and that the baryon-antibaryon interaction is more attractive than the baryon-baryon interaction. Sea quarks play a minor important role.

Towards a Topological Mechanism of Quark Confinement

(Received February 1, 2008)We report on new analyses of the topological and chiral vacuum structure of four-dimensional QCD on the lattice. Correlation functions as well as visualization of monopolecurrents in the maximally Abelian gauge emphasize their topological origin and gauge invari-ant characterization. The (anti)selfdual character of strong vacuum fluctuations is reveiledby smoothing. In full QCD, (anti)instanton positions are also centers of the local chiralcondensate and quark charge density. Most results turn out generically independent of theaction and the cooling/smoothing method.

Topological charges and confinement in lattice QCD

Abstract Topological properties of the QCD vacuum were studied on a lattice in the quenched approximation. Simulations were performed on an 8 3 × 4 lattice, with SU(3) Wilson action, at β = 5.6 (confinement phase) and β = 5.8 (deconfinement phase). Topological charges were measured using two local operators of the charge density and the method of cooling. Topological contents of vacuum configurations were found substantially different below and above the phase transition. We observed in both phases a suppression of topological fluctuations in the vicinity of static quarks and mesons. In the confinement phase the suppression occurs in the whole flux tube between the static quark and antiquark.

Vacuum polarization in compact QED

Abstract 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.

Observables of lattice gauge theory in minkowski space

Abstract U(1) gauge fields are decomposed into a monopole and photon part across the phase transition from the confinement to the Coulomb phase. We analyze the leading Lyapunov exponents of such gauge field configurations on the lattice which are initialized by quantum Monte Carlo simulations. We observe that the monopole field carries the same Lyapunov exponent as the original U(1) field. Evidence is found that monopole fields stay chaotic in the continuum whereas the photon fields are regular. First results are presented for the full spectrum of Lyapunov exponents of the U(1) gauge system.

Lyapunov exponents in Minkowskian U(1) gauge theory

Abstract U(1) gauge fields are decomposed into a monopole and photon part across the phase transition from the confinement to the Coulomb phase. We analyze the leading Lyapunov exponents of such gauge field configurations on the lattice which are initialized by quantum Monte Carlo simulations. We observe that the monopole field carries the same Lyapunov exponent as the original U(1) field. Evidence is found that monopole fields stay chaotic in the continuum whereas the photon fields are regular.

Zero modes of the QED Neuberger Dirac operator

Abstract We consider 4 d compact lattice QED in the quenched approximation. First, we briefly summarize the spectrum of the staggered Dirac operator and its connection with random matrix theory. Afterwards we present results for the low-lying eigenmodes of the Neuberger overlap-Dirac operator. In the strong coupling phase we find exact zero-modes. Subsequently we discuss possibly related topological excitations of the U(1) lattice gauge theory.

Distribution of fermionic and topological observables on the lattice

Abstract We analyze the topological and fermionic vacuum structure of four-dimensional QCD on the lattice by means of correlators of fermionic observables and topological densities. We show the existence of strong local correlations between the topological charge and monopole density on the one side and the quark condensate, charge and chiral density on the other side. Visualization of individual gauge configurations demonstrates that instantons (antiinstantons) carry positive (negative) chirality, whereas the quark charge density fluctuates in sign within instantons.