Constituent Gluon Content of the Static Quark-Antiquark State in Coulomb Gauge

Motivated by the gluon-chain model of flux tube formation, we compute and diagonalize the transfer matrix in lattice SU(2) gauge theory for states containing heavy static quark-antiquark sources, with separations up to one fermi. The elements of the transfer matrix are calculated by variational Monte Carlo methods, in a basis of states obtained by acting on the vacuum state with zero, one, and two-gluon operators in Coulomb gauge. The color Coulomb potential is obtained from the zero gluon to zero gluon element of the transfer matrix, and it is well-known that while this potential is asymptotically linear, it has a slope which is two to three times larger than the standard asymptotic string tension. We show that the addition of one and two gluon states results in a potential which is still linear, but the disagreement with the standard asymptotic string tension is reduced to 38% at the largest lattice coupling we have studied

Vortices, Symmetry Breaking, and Temporary Confinement in SU(2) Gauge-Higgs Theory

We further investigate center vortex percolation and Coulomb gauge remnant symmetry breaking in the SU(2) gauge-Higgs model. We show that string breaking is visible in Polyakov line correlators on the center projected lattice, that our usual numerical tests successfully relate P-vortices to center vortices, and that vortex removal removes the linear potential, as in the pure gauge theory. This data suggests that global center symmetry is not essential to the vortex confinement mechanism. But we also find that the line of vortex percolation-depercolation transitions, and the line of remnant symmetry breaking transitions, do not coincide in the SU(2)-Higgs phase diagram. This non-uniqueness of transition lines associated with non-local order parameters favors a straightforward interpretation of the Fradkin-Shenker theorem, namely: there is no unambiguous distinction, in the SU(2) gauge-Higgs models, between a "confining" phase and a Higgs phase.Comment: 8 pages, 11 figure

Adventures in Coulomb Gauge

We study the phase structure of SU(2) gauge theories at zero and high temperature, with and without scalar matter fields, in terms of the symmetric/broken realization of the remnant gauge symmetry which exists after fixing to Coulomb gauge. The symmetric realization is associated with a linearly rising color Coulomb potential (which we compute numerically), and is a necessary but not sufficient condition for confinement.Comment: 12 pages. Talk at Confinement 2003, Tokyo, July 21-2

The QCD vacuum wave functional and confinement in Coulomb gauge

We report results on the Coulomb-gauge ghost propagator and the color-Coulomb potential computed in two lattice gauge-field ensembles: (1) configurations derived from our recently proposed Yang-Mills vacuum wave functional in 2+1 dimensions, and (2) lattices generated by Monte Carlo simulations of the three-dimensional Euclidean SU(2) lattice gauge theory with the Wilson action. We observe remarkable agreement between the ghost propagators in both ensembles, but some differences in the potentials. Those originate from rare configurations with very small values of the lowest eigenvalue of the Coulomb-gauge Faddeev-Popov operator. If the same cuts on such exceptional configurations are applied in both ensembles, then the color-Coulomb potentials are also in reasonably good agreement.Comment: 7 pages, 4 figures (7 EPS files). Presented at the XXVIII International Symposium on Lattice Field Theory (Vacuum Structure and Confinement), June 14-19, 2010, Villasimius, Sardinia, Ital

Relations between the Gribov-horizon and center-vortex confinement scenarios

We review numerical evidence on connections between the center-vortex and Gribov-horizon confinement scenarios.Comment: Plenary talk presented by S. Olejnik at "Quark Confinement and the Hadron Spectrum VI", Villasimius, Sardinia, Italy, Sep. 21-25, 2004; 10 pages, 11 EPS figures, uses AIP Proceedings style file