Richard W. Haymaker

Structure of Abrikosov vortices in SU(2) lattice gauge theory

Abstract We calculate the electric flux and magnetic monopole current distribution in the presence of a static quark-antiquark pair of SU(2) lattice gauge theory in the maximal Abelian gauge. The current distribution confines the flux in a dual Abrikosov vortex whose core size is comparable to the flux penetration depth. The observed structure is described by a dual Ginzburg-Landau model.

Confinement studies in lattice QCD

Abstract We describe the current search for confinement mechanisms in lattice QCD. We report on a recent derivation of a lattice Ehrenfest–Maxwell relation for the Abelian projection of SU(2) lattice gauge theory. This gives a precise lattice definition of field strength and electric current due to static sources, charged dynamical fields, gauge fixing and ghosts. In the maximal Abelian gauge the electric charge is anti-screened analogously to the non-Abelian charge.

Distribution of the color fields around static quarks: Flux tube profiles.

We report detailed calculations of the profiles of energy and action densities in the quark-antiquark string in SU(2) lattice gauge theory. We conclude that at a {ital q}-{ital q}{vert_bar} separation {ital R}{approx_equal}1.0 fm we are beginning to see the asymptotic flux tube. By employing the Michael sum rules we further conclude that the peak energy density approaches a constant in {ital R}. {copyright} {ital 1995 The American Physical Society.}

London relation and fluxoid quantization for monopole currents in U(1) lattice gauge theory

We explore the mechanism of quark confinement in four-dimensional U(1) lattice gauge theory by measuring the color-magnetic current distribution from Dirac magnetic monopoles in the presence of a static quark-antiquark pair. Our results give the first direct evidence that the quarks induce a solenoidal current distribution that screens the color-electric flux of the quarks in an electric analogue of the Meissner effect in a superconductor. We show that the vacuum state of U(1) lattice gauge theory obeys both a dual version of the London equation and an electric fluxoid quantization condition.

SU(2) flux distributions on finite lattices.

We studied SU(2) flux distributions on four-dimensional Euclidean lattices with one dimension very large. By choosing the time direction appropriately we can study physics in two cases: one is finite volume in the zero-temperature limit, another is finite temperature in the intermediate to large volume limit. We found that for cases of [beta][gt][beta][sub [ital c]] there is no intrinsic string formation. Our lattices with [beta][gt][beta][sub [ital c]] belong to the intermediate volume region, and the string tension in this region is due to finite volume effects. In large volumes we found evidence for intrinsic string formation.

Dual vortices and gauge choice in Abelian projected SU(2) lattice gauge theory

We explore vortex formation for Abelian projected SU(2) in the Polyakov gauge and compare the results with those calculated in the maximal Abelian gauge. In both gauges, a nonzero vacuum expectation value of a monopole field operator signals confinement. We find vortices in the Polyakov projection, confirming the connection between the dual superconductor order parameter and the existence of vortices. However, we find that the Polyakov Abelian projection is problematic, leaving the maximal Abelian projection as the best candidate to define an effective theory of confinement in this scenario. {copyright} {ital 1997} {ital The American Physical Society}

Measurement of the penetration depth and coherence length in U(1) and SU(2) dual Abrikosov vortices

Abstract We calculate the electric field and the curl of the magnetic monopole current for U(1) and for SU(2) in the maximal Abelian gauge in the mid-plane between a quark antiquark pair. The results can be understood as a dual Abrikosov vortex in the Ginzburg-Landau theory.

Bag confinement chiral breaking effect on a goldstone pion

Abstract We present a model in which the pion is a bound-state Goldstone boson in QCD and then the quarks are confined by a MIT bag-like boundary condition. We depart from the MIT cavity approximation in that we dynamically break chiral symmetry prior to confinement and we confine only in the q q relative coordinate, leaving translation invariance in the total coordinate. We find M π = 120 MeV, and a bag diameter R π =7 GeV −1 .

Model independent approach to studies of the confining dual Abrikosov vortex in SU(2) lattice gauge theory

We address the problem of determining the type I, type II or borderline dual superconductor behavior in maximal Abelian gauge

Disappearance of the Abrikosov vortex above the deconfining phase transition in SU(2) lattice gauge theory

SU(2)