Center vortex model for the infrared sector of Yang-Mills theory

A model for the infrared sector of SU(2) Yang-Mills theory, based on magnetic vortices represented by (closed) random surfaces, is presented. The model quantitatively describes both confinement (including the finite-temperature transition to a deconfined phase) and the topological susceptibility of the Yang-Mills ensemble. A first (quenched) study of the spectrum of the Dirac operator furthermore yields a behavior for the chiral condensate which is compatible with results obtained in lattice gauge theory.Comment: Lattice2001(confinement) proceedings, 3 pages, 3 ps figure

Center vortex model for the infrared sector of SU(3) Yang-Mills theory: Topological susceptibility

The topological susceptibility of the SU(3) random vortex world-surface ensemble, an effective model of infrared Yang-Mills dynamics, is investigated. The model is implemented by composing vortex world-surfaces of elementary squares on a hypercubic lattice, supplemented by an appropriate specification of vortex color structure on the world-surfaces. Topological charge is generated in this picture by writhe and self-intersection of the vortex world-surfaces. Systematic uncertainties in the evaluation of the topological charge, engendered by the hypercubic construction, are discussed. Results for the topological susceptibility are reported as a function of temperature and compared to corresponding measurements in SU(3) lattice Yang-Mills theory. In the confined phase, the topological susceptibility of the random vortex world-surface ensemble appears quantitatively consistent with Yang-Mills theory. As the temperature is raised into the deconfined regime, the topological susceptibility falls off rapidly, but significantly less so than in SU(3) lattice Yang-Mills theory. Possible causes of this deviation, ranging from artefacts of the hypercubic description to more physical sources, such as the adopted vortex dynamics, are discussed.Comment: 30 pages, 6 figure

Center vortex model for the infrared sector of SU(4) Yang-Mills theory: String tensions and deconfinement transition

A random vortex world-surface model for the infrared sector of SU(4) Yang-Mills theory is constructed, focusing on the confinement properties and the behavior at the deconfinement phase transition. Although the corresponding data from lattice Yang-Mills theory can be reproduced, the model requires a more complex action and considerably more tuning than the SU(2) and SU(3) cases studied previously. Its predictive capabilities are accordingly reduced. This behavior has a definite physical origin, which is elucidated in detail in the present work. As the number of colors is raised in Yang-Mills theory, the corresponding infrared effective vortex description cannot indefinitely continue to rely on dynamics determined purely by vortex world-surface characteristics; additional color structures present on the vortices begin to play a role. As evidenced by the modeling effort reported here, definite signatures of this behavior appear in the case of four colors.Comment: 24 pages, 7 figures containing 8 ps file

Center vortex model for the infrared sector of SU(3) Yang-Mills theory -- baryonic potential

The baryonic potential in the framework of the SU(3) random vortex world-surface model is evaluated for a variety of static color source geometries. For comparison, carefully taking into consideration the string tension anisotropy engendered by the hypercubic lattice description, also the Delta and Y law predictions for the baryonic potential are given. Only the Y law predictions are consistent with the baryonic potentials measured.Comment: 13 LaTeX pages, 2 figures (3 ps files). Replacement contains additional reference

Neutron electric polarizability from unquenched lattice QCD using the background field approach

A calculational scheme for obtaining the electric polarizability of the neutron in lattice QCD with dynamical quarks is developed, using the background field approach. The scheme differs substantially from methods previously used in the quenched approximation, the physical reason being that the QCD ensemble is no longer independent of the external electromagnetic field in the dynamical quark case. One is led to compute (certain integrals over) four-point functions. Particular emphasis is also placed on the physical role of constant external gauge fields on a finite lattice; the presence of these fields complicates the extraction of polarizabilities, since it gives rise to an additional shift of the neutron mass unrelated to polarizability effects. The method is tested on a SU(3) flavor-symmetric ensemble furnished by the MILC Collaboration, corresponding to a pion mass of m_pi = 759 MeV. Disconnected diagrams are evaluated using stochastic estimation. A small negative electric polarizability of alpha =(-2.0 +/- 0.9) 10^(-4) fm^3 is found for the neutron at this rather large pion mass; this result does not seem implausible in view of the qualitative behavior of alpha as a function of m_pi suggested by Chiral Effective Theory.Comment: 36 pages, 11 figures. Note added concerning analytic continuation in the external electric field; some notation made more precis

Energy Density of Vortices in the Schroedinger Picture

The one-loop energy density of an infinitely thin static magnetic vortex in SU(2) Yang-Mills theory is evaluated using the Schroedinger picture. Both the gluonic fluctuations as well as the quarks in the vortex background are included. The energy density of the magnetic vortex is discussed as a function of the magnetic flux. The center vortices correspond to local minima in the effective potential. These minima are degenerated with the perturbative vacuum if the fermions are ignored. Inclusion of fermions lifts this degeneracy, raising the vortex energy above the energy of the perturbative vacuum.Comment: 25 pages, 2 figure