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Richard W. Haymaker

Publications and source records attributed to Richard W. Haymaker.

At least 19 recordsLinked to original sources
arXiv2006

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 SU(2) through the study of the dual Abrikosov vortex. We find that significant electric currents in the simulation data call into question the use of the dual Ginzburg Landau Higgs model in interpreting the data. Further, two definitions of the penetration depth parameter take two different values. The splitting of this parameter into two is intricately connected to the existence of electric currents. It is important in our approach that we employ definitions of flux and electric and magnetic currents that respect Maxwell equations exactly for lattice averages independent of lattice spacings. Applied to specific Wilson loop sizes, our conclusions differ from those that use the dual GLH model.

hep-lat↗
arXiv2003

Consistency of lattice definitions of U(1) flux in Abelian projected SU(2) gauge theory

We reexamine the dual Abrikosov vortex under the requirement that the lattice averages of the fields satisfy exact Maxwell equations [ME]. The electric ME accounts for the total flux and the magnetic ME determines the shape of the confining string. This leads to unique and consistent definitions of flux and electric and magnetic currents at finite lattice spacing. The resulting modification of the standard DeGrand-Toussaint construction gives a magnetic current comprised of smeared monopoles.

hep-lat↗
arXiv2003

Consistent Definitions of Flux and Electric and Magnetic Current in Abelian Projected SU(2) Lattice Gauge Theory

Through the use of a lattice U(1) Ward-Takahashi identity, one can find a precise definition of flux and electric four-current that does not rely on the continuum limit. The magnetic four-current defined for example by the DeGrand-Toussaint construction introduces order a^2 errors in the field distributions. We advocate using a single definition of flux in order to be consistent with both the electric and magnetic Maxwell's equations at any lattice spacing. In a U(1) theory the monopoles are slightly smeared by this choice, i.e. are no longer associated with a single lattice cube. In Abelian projected SU(2) the consistent definition suggests further modifications. For simulations in the scaling window, we do not foresee large changes in the standard analysis of the dual Abrikosov vortex in the maximal Abelian gauge because the order a^2 corrections have small fluctuations and tend to cancel out. However in other gauges, the consequences of our definitions could lead to large effects which may help in understanding the choice of gauge. We also examine the effect of truncating all monopoles except for the dominant cluster on the profile of the dual Abrikosov vortex.

hep-lat↗
arXiv2002

Dual Abrikosov vortex between confined charges

We show that the dual Abrikosov vortex between quark and antiquark in Abelian Projected SU(2) gauge theory is insensitive to truncation of all loops except the large monopole cluster noted by Hart and Teper. As the transverse distance increases, the discrepancy decreases, suggesting that the London penetration depth determined by the tail is invariant under the truncation of short loops.

hep-lat↗
arXiv2002

Connections between Thin,Thick and Projection Vortices in SU(2) Lattice Gauge Theory

We elucidate the connection between $SO(3) \times Z(2)$ and the usual SU(2) configuration variables. By exploiting the freedom of choosing a particular SO(3) representative we find a direct connection between the two configuration spaces. We are then able to compare the Kovacs-Tomboulis formulation of center vortices with the projection vortex formulation on the same configuration. Choosing a different representative, and going to the maximal center gauge, we show that projection vortices occur without approximation. The projection vortex dominance approximation results from dropping a factor in an exact expression for the Wilson loop.

hep-lat↗
arXiv2001

Connection between Tomboulis vortices and projection vortices

By using the freedom of picking a representative we explore connections between the Tomboulis SO(3)xZ(2) form of the partition function and the SU(2) form. We are able to express the monopole and vortex observables of the former in terms of configurations of the latter. Also we can measure Tomboulis and projection vortex counters on the same configuration to search for correlations.

hep-lat↗
arXiv2001

Center vortices on SU(2) lattices

We show that gauge invariant definition of thin, thick and hybrid center vortices, defined by Kovacs and Tomboulis on SO(3) x Z(2) configurations, can also be defined in SU(2). We make this connection using the freedom of choosing a particular SU(2) representative of SO(3). We further show that in another representative the Tomboulis σ- ηthin vortices are P (projection) vortices. The projection approximation corresponds to dropping the perimeter factor of a Wilson loop after appropriate gauge fixing. We present results for static quark potentials based on these vortex counters and compare pojection vortex counters with gauge invariant ones on the same configuration.

hep-lat↗
arXiv2000

Vortices in SO(3)xZ(2) simulations

We study the configuration space of the Tomboulis $SO(3) \times Z(2)$ formulation with periodic boundary conditions. The dynamical variables are constrained by the required coincidence of Z(2) and SO(3) monopoles. We propose an update algorithm that satisfies the constraints and is straightforward to implement. We further prove that this it reaches all configurations. We show how the boundary conditions put constraints on the configuration space. We measure gauge invariant vortex counters for "thin", "thick" and "hybrid" vortex sheets. For comparison we also measure projection vortex counters defined in the maximal center gauge.

hep-lat↗
arXiv1998

Confinement studies in lattice QCD

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.

hep-lat↗
arXiv1998

Ehrenfest theorems and charge antiscreening in Abelian projected gauge theories

We derive exact relations for SU(2) lattice gauge theory in 3+1 dimensions. In terms of Abelian projection, these are the expectation values of Maxwell equations that define a new field strength operator and conserved, dynamic electric currents formed from the charged matter and ghost fields. The effect of gauge fixing is calculated, and in the maximally Abelian gauge we find antiscreening of U(1) Wilson loop source charges. We discuss the importance of these quantities in the dual superconducting vacuum mechanism of confinement.

hep-lat↗
arXiv1995

Dual Abrikosov vortices in U(1) and SU(2) lattice gauge theories

The spatial distribution of fields and currents in confining theories can give direct evidence of dual superconductivity. We review the behavior of vortices in the lattice Higgs effective theory. We discuss the techniques for finding these properties and calculating the superconductivity parameters in lattice simulations. We have seen dual Abrikosov vortices directly in pure U(1) and SU(2) and others have also seen them in SU(3). We review the duality transformation for U(1) in order to connect the U(1) results to a dual Higgs theory. In the non-Abelian cases the system appears to be near the borderline between type I and II. We also discuss the response of the persistent currents to external fields.

hep-lat↗
arXiv1995

Dual Abrikosov Vortices in Confining Theories

The spacial distribution of fields and currents in confining theories can give direct evidence of dual superconductivity. We would like to discuss the techniques for finding these properties and calculating the superconductivity parameters in lattice simulations. We have seen dual Abrikosov vortices directly in pure U(1) and SU(2) and others have also seen them in SU(3). In the non-Abelian cases the system appears to be near the borderline between type I and II. We also discuss the response of the supercurrents to external fields.

hep-lat↗
arXiv1995

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

We calculate the solenoidal magnetic monopole current and electric flux distributions at finite temperature in the presence of a static quark antiquark pair. The simulation was performed using SU(2) lattice gauge theory in the maximal Abelian gauge. We find that the monopole current and electric flux distributions are quite different below and above the finite temperature deconfining phase transition point and agree with predictions of the Ginzburg-Landau effective theory.

hep-lat↗
arXiv1993

SU(2) finite temperature phase transition and Michael sum rules

We studied the finite temperature phase transition of SU(2) gauge theory on four-dimensional Euclidean lattices by Monte Carlo simulations, and measured the flux distributions of a $q\bar q$ pair in both confined and unconfined phases. We reviewed and generalized Michael sum rules to include finite temperature effects. To compare our flux data with predictions of Michael sum rules, we studied the behavior of string tension with temperature. Our data agree well with the generalized sum rules.

hep-lat↗
arXiv1993

Vacuum structure of pure gauge theories on the lattice

We present results from simulations on two aspects of quark confinement in the pure gauge sector. First is the calculation of the profile of the flux tube connecting a static $q \bar{q}$ pair in $SU(2)$. By using the Michael sum rules as a constraint we give evidence that the energy density at the center of the flux tube goes to a constant as a function of quark separation. Slow variation of the width and energy density is not ruled out. Secondly in the confined phase of lattice $U(1)$ we calculate the curl of the magnetic monopole current and show that the dual London equation is satisfied and that the electric fluxoid is quantized.

hep-lat↗
arXiv1993

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 the intermediate to large volume limit. We found that for cases of beta > beta crit there is no intrinsic string formation. Our lattices with beta > beta crit belong to 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.

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