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H. Reinhardt

Publications and source records attributed to H. Reinhardt.

At least 91 records · Page 5Linked to original sources
arXiv2001

Gluon propagators and quark confinement

The gluon propagator is investigated in Landau and in maximal center gauge for the gauge group SU(2) by means of lattice gauge simulations. We find that Gribov ambiguities arising from the implementation of Landau gauge have a small influence on the propagator. In agreement with previous findings, we obtain that the small momentum behavior is dominated by a mass, which is of order $(1.48 \pm 0.05) \sqrtσ$, where $σ$ is the string tension. By removing the confining vortices from the full Yang-Mills ensemble, we convert full YM-theory into a theory which does not confine quarks. We find that in the latter case the strength of the gluon propagator in the intermediate momentum range is strongly reduced. The spectral functions which reproduce the numerical data for the propagators are analyzed using a generalized Maximum Entropy Method.

hep-ph↗
arXiv2001

Singular gauge potentials and the gluon condensate at zero temperature

We consider a new cooling procedure which separates gluon degrees of freedom from singular center vortices in SU(2) LGT in a gauge invariant way. Restricted by a cooling scale $κ^4/σ^2$ fixing the residual SO(3) gluonic action relative to the string tension, the procedure is RG invariant. In the limit $κ\to 0$ a pure Z(2) vortex texture is left. This {\it minimal} vortex content does not contribute to the string tension. It reproduces, however, the lowest glueball states. With an action density scaling like $a^4$ with $β$, it defines a finite contribution to the action density at T=0 in the continuum limit. We propose to interpret this a mass dimension 4 condensate related to the gluon condensate. Similarly, this vortex texture is revealed in the Landau gauge.

hep-lat↗
arXiv2001

Gauge potential singularities and the gluon condensate at finite temperatures

The continuum limit of SU(2) lattice gauge theory is carefully investigated at zero and at finite temperatures. It is found that the continuum gauge field has singularities originating from center degrees of freedom being discovered in Landau gauge. Our numerical results show that the density of these singularities properly extrapolates to a non-vanishing continuum limit. The action density of the non-trivial Z_2 links is tentatively identified with the gluon condensate. We find for temperatures larger than the deconfinement temperature that the thermal fluctuations of the embedded Z_2 gauge theory result in an increase of the gluon condensate with increasing temperature.

hep-lat↗
arXiv2001

Manifestation of Confinement in the Gluon propagator

The gluon propagator in Landau gauge is calculated on the lattice for SU(2) gauge theory. In particular the manifestation of confinement in the gluon propagator is studied. Removing the confining center vortices from the Yang-Mills ensemble leads to a drastic reduction of the gluonic form factor in the intermediate momentum regime.

hep-lat↗
arXiv2001

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.

hep-lat↗
arXiv2001

Gauge invariant Z_2 vortex vacuum textures and the SU(2) gluon condensate

For SU(2) lattice gauge theory, a new SO(3) cooling procedure is proposed which removes the SU(2)/Z(2) coset fields from the lattice configurations and reveals a Z(2) vortex vacuum texture different from the P-vortex content obtained in the maximal center gauge. Cooling can be restricted in a renormalization group invariant way by a parameter controlling the remaining SO(3) action density. A gauge invariant Z(2) vortex vacuum emerges asymptotically if cooling is not restricted. This ``vortex texture'' does not support the string tension or a finite part of it. The SU(2) action density associated with the new Z(2) vortex texture has a smooth extrapolation to the continuum limit. We propose an interpretation as a mass dimension four condensate related to the gluon condensate featuring in the operator product expansion.

hep-lat↗
arXiv2001

Production Processes as a Tool to Study Parameterizations of Quark Confinement

We introduce diquarks as separable correlations in the two-quark Green's function to facilitate the description of baryons as relativistic three-quark bound states. These states then emerge as solutions of Bethe-Salpeter equations for quarks and diquarks that interact via quark exchange. When solving these equations we consider various dressing functions for the free quark and diquark propagators that prohibit the existence of corresponding asymptotic states and thus effectively parameterize confinement. We study the implications of qualitatively different dressing functions on the model predictions for the masses of the octet baryons as well as the electromagnetic and strong form factors of the nucleon. For different dressing functions we in particular compare the predictions for kaon photoproduction, $γp\to KΛ$, and associated strangeness production, $pp\to pKΛ$ with experimental data. This leads to conclusions on the permissibility of different dressing functions.

hep-ph↗
arXiv2001

Center vortex properties in the Laplace center gauge of SU(2) Yang-Mills theory

Resorting to the the Laplace center gauge (LCG) and to the Maximal-center gauge (MCG), respectively, confining vortices are defined by center projection in either case. Vortex properties are investigated in the continuum limit of SU(2) lattice gauge theory. The vortex (area) density and the density of vortex crossing points are investigated. In the case of MCG, both densities are physical quantities in the continuum limit. By contrast, in the LCG the piercing as well as the crossing points lie dense in the continuum limit. In both cases, an approximate treatment by means of a weakly interacting vortex gas is not appropriate.

hep-lat↗
arXiv2000

Abelian and center gauges in continuum Yang-Mills-Theory

Abelian and center gauges are considered in continuum Yang-Mills theory in order to detect the magnetic monopole and center vortex content of gauge field configurations. Specifically we examine the Laplacian Abelian and center gauges, which are free of Gribov copies, as well as the center gauge analog of the (Abelian) Polyakov gauge. In particular, we study meron, instanton and instanton-anti-instanton field configurations in these gauges and determine their monopole and vortex content. While a single instanton does not give rise to a center vortex, we find center vortices for merons. Furthermore we provide evidence, that merons can be interpreted as intersection points of center vortices. For the instanton-anti-instanton pair, we find a center vortex enclosing their centers, which carries two monopole loops.

hep-th↗
arXiv2000

Center Vortices in Continuum Yang-Mills Theory

The properties of center vortices are discussed within continuum Yang-Mills theory. By starting from the lattice theory and carefully performing the continuum limit the gauge potential of center vortices is obtained and the continuum analog of the maximal center gauge fixing is extracted. It is shown, that the Pontryagin index of center vortices is given by their self-intersection number, which vanishes unless the center vortices host magnetic monpoles, which make the vortex sheets non-oriented.

hep-th↗
arXiv2000

Recent results in the 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 and the topological aspects of Yang-Mills theory. Details (including an adequate list of references) can be found in hep-lat/9912003 and hep-lat/0004013, both to appear in Nucl. Phys. B.

hep-lat↗
arXiv2000

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 random surfaces, governed by an action penalizing curvature, are investigated using Monte Carlo methods on a hypercubic lattice. A low-temperature confining phase and a high-temperature deconfined phase are generated by this simple dynamics. After fixing the parameters of the model such as to reproduce the relation between deconfinement temperature and zero-temperature string tension found in lattice Yang-Mills theory, a surprisingly accurate prediction of the spatial string tension in the deconfined phase results. Furthermore, the Pontryagin index associated with the lattice random surfaces of the model is constructed. This allows to also predict the topological susceptibility; the result is compatible with measurements in lattice Yang-Mills theory. Thus, for the first time an effective model description of the infrared sector emerges which simultaneously and consistently reproduces both confinement and the topological aspects of Yang-Mills theory within a unified framework. Further details can be found in hep-lat/9912003 and hep-lat/0004013, both to appear in Nucl. Phys. B.

hep-th↗
arXiv2000

Center-vortex dominance after dimensional reduction of SU(2) lattice gauge theory

The high-temperature phase of SU(2) Yang-Mills theory is addressed by means of dimensional reduction with a special emphasis on the properties of center vortices. For this purpose, the vortex vacuum which arises from center projection is studied in pure 3-dimensional Yang-Mills theory as well as in the 3-dimensional adjoint Higgs model which describes the high temperature phase of the 4-dimensional SU(2) gauge theory. We find center-dominance within the numerical accuracy of 10%.

hep-lat↗
arXiv2000

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

A model for the infrared sector of Yang-Mills theory based on magnetic vortices represented by (closed) random surfaces is investigated using lattice Monte Carlo methods. The random surfaces are governed by a surface area action and a curvature action. The model generates a finite-temperature deconfinement transition; the coupling constants of the model can be chosen such as to reproduce the SU(2) Yang-Mills ratio of the deconfinement temperature to the square root of the zero-temperature string tension, T_c / sqrt{sigma_0} =0.69. This yields a physical trajectory in the space of coupling constants on which the confinement properties are approximately invariant. An at first sight surprisingly accurate prediction of the spatial string tension in the deconfined phase results, which can be made plausible in view of the specific space-time structure of the vortex configurations in this phase. The confinement properties are shown to be intimately tied to the percolation properties of the vortex surfaces.

hep-lat↗
arXiv1999

Magnetic Monopoles, Center Vortices, Confinement and Topology of Gauge Fields

The vortex picture of confinement is studied. The deconfinement phase transition is explained as a transition from a phase in which vortices percolate to a phase of small vortices. Lattice results are presented in support of this scenario. Furthermore the topological properties of magnetic monopoles and center vortices arising, respectively, in Abelian and center gauges are studied in continuum Yang-Mills-theory. For this purpose the continuum analog of the maximum center gauge is constructed.

hep-th↗
arXiv1999

Quantum gauge fixing and vortex dominance

We introduce quantum gauge fixing (QGF) as a new class of gauge fixings. While the maximal center gauge might not show vortex dominance, the confining properties of the vortices observed in past lattice calculations are argued to have been obtained in a gauge more akin to QGF than to the strict maximal center gauge.

hep-lat↗