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J. Greensite

Publications and source records attributed to J. Greensite.

At least 19 recordsLinked to original sources
arXiv2013

Testing the Yang-Mills vacuum wave functional Ansatz in 3+1 dimensions

We proposed a simple Ansatz for the vacuum wave functional (VWF) of SU(2) gauge theory in temporal gauge. In 2+1 dimensions, the Ansatz was shown to be a fairly good approximation to the true VWF of the theory. Relative probabilities of various test configurations in the vacuum can be computed in numerical simulations of lattice-regulated SU(2) gauge theory by the method proposed long ago by Greensite and Iwasaki. We report promising (albeit still preliminary) results of testing the proposed VWF in 3+1 dimensions on various sets of lattice gauge field configurations.

hep-lat↗
arXiv2013

Effective Polyakov line action from the relative weights method

We apply the relative weights method (arXiv:1209.5697) to determine the effective Polyakov line action for SU(2) lattice gauge theory in the confined phase, at lattice coupling beta=2.2 and N_t=4 lattice spacings in the time direction. The effective action turns out to be bilinear in the fundamental representation Polyakov line variables, with a rather simple expression for the finite range kernel. The validity of this action is tested by computing Polyakov line correlators, via Monte Carlo simulation, in both the effective action and the underlying lattice theory. It is found that the correlators in each theory are in very close agreement.

hep-lat↗
arXiv2011

Measurements of the Yang-Mills vacuum wavefunctional, and related studies

I present numerical tests of several recent proposals for the Yang-Mills vacuum wavefunctional in D=2+1 dimensions. In these tests the predicted relative values of the squared wavefunctional, evaluated on a finite set of abelian plane wave and non-abelian constant configurations, are compared to the corresponding values for the true ground state, extracted from Monte Carlo simulations. I also study how the 2+1 dimensional color Coulomb potential, averaged over a set of simple trial configurations, varies with the proximity of those configurations to the Gribov horizon.

hep-lat↗
arXiv2011

k-String tensions and their large-N dependence

We consider whether the 1/N corrections to k-string tensions must begin at order 1/N^2, as in the Sine Law, or whether odd powers of 1/N, as in Casimir Scaling, are also acceptable. The issue is important because different models of confinement differ in their predictions for the representation-dependence of k-string tensions, and corrections involving odd powers of 1/N would seem to be ruled out by the large-N expansion. We show, however, that k-string tensions may, in fact, have leading 1/N corrections, and consistency with the large-N expansion, in the open string sector, is achieved by an exact pairwise cancellation among terms involving odd powers of 1/N in particular combinations of Wilson loops. It is shown how these cancellations come about in a concrete example, namely, strong coupling lattice gauge theory with the heat-kernel action, in which k-string tensions follow the Casimir scaling rule.

hep-lat↗
arXiv2011

Adjoint torelons, and the persistence of color electric flux tubes in the deconfined phase

It is argued that the adjoint torelon loop, i.e. a Polyakov loop in the adjoint representation running in a spatial, rather than temporal, direction, is an observable which is sensitive to the presence of long color electric flux tubes at high temperatures. We show via lattice Monte Carlo simulations that this observable has a sharp peak at the deconfinement transition, remains much larger than the vacuum value for some range of $T>T_c$, and falls below the vacuum value for $T > 2T_c$. This result suggests that long electric flux tubes may persist for a finite range of temperatures past the deconfinement transition, and at some stage disappear, presumably melting into a plasma of gluons. As a side remark, we point out that our results at $T<T_c$ imply that the eigenvalues of ordinary Polyakov loop holonomies in the confinement phase have a slight tendency to attract rather than repel, which may be relevant to certain models of confinement.

hep-lat↗
arXiv2011

In quest of the Yang-Mills vacuum wavefunctional

A simple recursion procedure was devised to generate lattice configurations with probability distributions given by simple approximate Yang-Mills vacuum wavefunctionals. A few quantities determined in ensembles of these configurations are compared to those computed in configurations generated in standard Monte Carlo simulations of the three-dimensional Yang-Mills theory.

hep-lat↗
arXiv2011

Testing Proposals for the Yang-Mills Vacuum Wavefunctional by Measurement of the Vacuum

We review a method, suggested many years ago, to numerically measure the relative amplitudes of the true Yang-Mills vacuum wavefunctional in a finite set of lattice-regulated field configurations. The technique is applied in 2+1 dimensions to sets of abelian plane wave configurations of varying amplitude and wavelength, and sets of non-abelian constant configurations. The results are compared to the predictions of several proposed versions of the Yang-Mills vacuum wavefunctional that have appeared in the literature. These include (i) a suggestion in temporal gauge due to Greensite and Olejnik; (ii) the "new variables" wavefunction put forward by Karabali, Kim, and Nair; (iii) a hybrid proposal combining features of the temporal gauge and new variables wavefunctionals; and (iv) Coulomb gauge wavefunctionals developed by Reinhardt and co-workers, and by Szczepaniak and co-workers. We find that wavefunctionals which simplify to a "dimensional reduction" form at large scales, i.e. which have the form of a probability distribution for two-dimensional lattice gauge theory, when evaluated on long-wavelength configurations, have the optimal agreement with the data.

hep-lat↗
arXiv2011

Panel discussion: What {\it don't} we know about confinement?

The participants in this discussion session of the QCHS 9 meeting were each asked the following question: "What would be the most useful piece of information that you could obtain, by whatever means, that would advance your own program, and/or our general understanding of confinement?" This proceedings contains a brief summary of each panel member's contribution to the discussion, provided by the panel members themselves.

hep-th↗
arXiv2010

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.

hep-lat↗
arXiv2010

Coulomb Confinement from the Yang-Mills Vacuum State in 2+1 Dimensions

The Coulomb-gauge ghost propagator, and the color-Coulomb potential, are computed in an ensemble of configurations derived from our recently proposed Yang-Mills vacuum wavefunctional in 2+1 dimensions. The results are compared to the corresponding values obtained by standard Monte Carlo simulations in three Euclidean dimensions. The agreement is quite striking for the Coulomb-gauge ghost propagator. The color-Coulomb potential rises linearly at large distances, but its determination suffers from rather large statistical fluctuations, due to configurations with very low values of $μ_0$, the lowest eigenvalue of the Coulomb-gauge Faddeev-Popov operator. However, if one imposes cuts on the data, effectively leaving out configurations with very low $μ_0$, the agreement of the potential in both sets of configurations is again satisfactory, although the errorbars grow systematically as the cutoff is eliminated.

hep-lat↗
arXiv2010

Faddeev-Popov spectra at the Gribov horizon

I present a perturbative calculation of the spectrum of the Faddeev-Popov operator in Coulomb gauge in three dimensions, and Landau gauge in two and three dimensions, with an ansatz for the gluon propagator as the non-perturbative input. The results show how the low-lying Faddeev-Popov eigenvalue spectrum is modified as the first Gribov horizon is approached, and how the spectra can differ in Coulomb and Landau gauges.

hep-th↗
arXiv2009

Gluon chains and the quark-antiquark potential

The flux tube between a quark and an antiquark in Coulomb gauge is imagined in the gluon-chain model as a sequence of constituent gluons bound together by Coulombic nearest-neighbor interactions. We diagonalize the transfer matrix in SU(2) lattice gauge theory in a finite basis of states containing a static quark-antiquark pair together with zero, one, and two gluons in Coulomb gauge. We show that while the string tension of the color-Coulomb potential (obtained from the zero-gluon to zero-gluon element of the transfer matrix) overshoots the true asymptotic string tension by a factor of about three, the inclusion of a few states with constituent gluons reduces the discrepancy considerably. The minimal energy eigenstate of the transfer matrix in the zero-, one-, and two-gluon basis exhibits a linearly rising potential with the string tension only about 1.4 times larger than the asymptotic one.

hep-lat↗
arXiv2009

Gauge Orbits and the Coulomb Potential

If the color Coulomb potential is confining, then the Coulomb field energy of an isolated color charge is infinite on an infinite lattice, even if the usual UV divergence is lattice regulated. A simple criterion for Coulomb confinement is that the expectation value of timelike link variables vanishes in Coulomb gauge, but it is unclear how this criterion is related to the spectrum of the corresponding Faddeev-Popov operator, which can be used to formulate a quite different criterion for Coulomb confinement. The purpose of this article is to connect the two seemingly different Coulomb confinement criteria, and explain the geometrical basis of the connection.

hep-lat↗
arXiv2009

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.

hep-lat↗
arXiv2008

Center vortex influence on the Dirac spectrum

We study the influence of center vortices on the low-lying eigenmodes of the Dirac operator, in both the overlap and asqtad formulations. For center-projected configurations, one finds that the low-lying near-zero modes are present in the staggered (asqtad) formulation, but not in the overlap and "chirally-improved" formulations. We argue that this is due to the absence of a field-independent chiral symmetry in the latter formulations, when the Dirac operator is evaluated on the very rough configurations generated by center projection. We also confirm and extend the results of Kovalenko et al. [Phys. Lett. B 648, 383 (2007)], finding strong correlations between center vortex locations, and the scalar density of low-lying Dirac eigenmodes on unprojected lattices, in both asqtad and overlap formulations. It is found that the low-lying eigenmodes have their largest concentrations in point-like regions, rather than on submanifolds of higher dimensionality.

hep-lat↗
arXiv2008

Is Confinement a Phase of Broken Dual Gauge Symmetry?

We study whether broken dual gauge symmetry, as detected by a monopole order parameter introduced by the Pisa group, is necessarily associated with the confinement phase of a lattice gauge theory. We find a number of examples, including SU(2) gauge-Higgs theory, mixed fundamental-adjoint SU(2) gauge theory, and pure SU(5) gauge theory, which appear to indicate a dual gauge symmetry transition in the absence of a transition to or from a confined phase. While these results are not necessarily fatal to the dual superconductor hypothesis, they may pose some problems of interpretation for the present formulation of the Pisa monopole criterion.

hep-lat↗
arXiv2008

Dimensional Reduction and the Yang-Mills Vacuum State in 2+1 Dimensions

We propose an approximation to the ground state of Yang-Mills theory, quantized in temporal gauge and 2+1 dimensions, which satisfies the Yang-Mills Schrodinger equation in both the free-field limit, and in a strong-field zero mode limit. Our proposal contains a single parameter with dimensions of mass; confinement via dimensional reduction is obtained if this parameter is non-zero, and a non-zero value appears to be energetically preferred. A method for numerical simulation of this vacuum state is developed. It is shown that if the mass parameter is fixed from the known string tension in 2+1 dimensions, the resulting mass gap deduced from the vacuum state agrees, to within a few percent, with known results for the mass gap obtained by standard lattice Monte Carlo methods.

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