arXiv subjects

M. Faber

Publications and source records attributed to M. Faber.

At least 91 records · Page 5Linked to original sources

arXiv1999

Some Insights into the Method of Center Projection

We present several new results which pertain to the successes of center projection in maximal center gauge (MCG). In particular, we show why any center vortex, inserted "by hand" into a thermalized lattice configuration, will be among the set of vortices found by the center projection procedure. We show that this "vortex-finding property" is lost when gauge-field configurations are fixed to Landau gauge prior to the maximal center gauge fixing; this fact accounts for the loss of center dominance in the corresponding projected configurations. Variants of maximal center (adjoint Landau) gauge are proposed which correctly identify relevant center vortices.

hep-lat↗

arXiv1999

The Structure of Projected Center Vortices in Lattice Gauge Theory

We investigate the structure of center vortices in maximal center gauge of SU(2) lattice gauge theory at zero and finite temperature. In center projection the vortices (called P-vortices) form connected two dimensional surfaces on the dual four-dimensional lattice. At zero temperature we find, in agreement with the area law behaviour of Wilson loops, that most of the P-vortex plaquettes are parts of a single huge vortex. Small P-vortices, and short-range fluctuations of the large vortex surface, do not contribute to the string tension. All of the huge vortices detected in several thousand field configurations turn out to be unorientable. We determine the Euler characteristic of these surfaces and find that they have a very irregular structure with many handles. At finite temperature P-vortices exist also in the deconfined phase. They form cylindric objects which extend in time direction. After removal of unimportant short range fluctuations they consist only of space-space plaquettes, which is in accordance with the perimeter law behaviour of timelike Wilson loops, and the area law behaviour of spatial Wilson loops in this phase.

hep-lat↗

arXiv1999

On the Deconfinement Phase Transition in Hot Gauge Theories with Dynamical Matter Fields

The phase structure of hot gauge theories with dynamical matter fields is reexamined in the canonical ensemble with respect to triality. Since this ensemble implies a projection to the zero triality sector of the theory we introduce a proper quantity which is able to reveal a critical behaviour of the theory with fundamental quarks. We discuss the properties of both the chromoelectric and chromomagnetic sectors of the theory and show while electric charges carrying a unit of Z(N) charge are screened at high temperatures by dynamical matter loops, this is not the case for the Z(N) magnetic flux. An order parameter is constructed to probe the realization of local discrete Z(N) symmetry in the magnetic sector. We argue it can be used to detect a deconfinement phase being defined in terms of the screening mechanism as a phase of unscreened Z(N) flux. It may be detectable at long range via the Aharonov-Bohm effect. We discuss the possible phase structure of QCD in this approach.

hep-lat↗

arXiv1998

Solar neutrino processes in the relativistic field theory model of the deuteron

The generalized version of the relativistic field theory model of the deuteron (RFMD) is applied to the description of processes of astrophysical interest and low-energy elastic NN scattering. The value of the astrophysical factor S_{pp}(0) = 5.52x10^{-25} MeV b is found to be enhanced by a factor of 1.42 with respect to the classical value S^*_{pp}(0) = 3.89x10{-25} MeV b obtained by Kamionkowski and Bahcall in the potential model approach (PMA). The astrophysical aspects of this enhancement are discussed. The cross sections for the disintegration of the deuteron by (anti-) neutrinos nu_e + D -> e^- + p + p, anti-nu_e + D -> e^+ + n + n and nu_e(anti-nu_e) + D -> nu_e(anti-nu_e) + n + p are calculated for the energies of (anti-) neutrinos ranging from thresholds up to 10 MeV. The results are discussed in comparison with the PMA data. The cross sections for anti-nu_e + D -> e^+ + n + n and anti-nu_e + D -> anti-nu_e + n + p averaged over the reactor anti-neutrino energy spectrum agree well with experimental data. The astrophysical factor S_{pep}(0) for the process p + e^- + p -> nu_e + D (or pep-process) is calculated relative to S_{pp}(0) in complete agreement with the result obtained by Bahcall and May. The reaction rate for the neutron-proton radiative capture is calculated in agreement with the PMA result obtained for pure M1 transition. It is shown that in the RFMD one can describe low--energy elastic NN scattering in complete agreement with low-energy nuclear phenomenology.

nucl-th↗

arXiv1998

Solar proton burning, photon and anti-neutrino disintegration of the deuteron in the relativistic field theory model of the deuteron

The relativistic field theory model of the deuteron (RFMD) is applied to the calculation of the astrophysical factor S_{pp}(0) for the process of the solar proton burning p + p -> D + e^+ + ν_e and the cross sections for the disintegration of the deuteron by photons gamma + D -> n + p and anti-neutrinos \barν_e + D -> e^+ + n + n. Our theoretical value of the astrophysical factor S_{pp}(0) = 4.02 x 10^{-25} MeV b agrees with the classical result obtained by Bahcall and Kamionkowski S_{pp}(0) = 3.89 x 10^{-25} MeV b in the potential model approach (PMA). The cross sections for the disintegration of the deuteron by photons and anti-neutrinos calculated near thresholds are in good agreement with the PMA. An extrapolation of the cross sections for energies far from thresholds is suggested and related to the inclusion of form factors describing spatial smearing of the deuteron and the NN system. The extrapolated cross section for the disintegration of the deuteron by anti-neutrinos agrees with that calculated in the PMA in the anti-neutrino energy region from threshold up to 10 MeV. The extrapolated cross section averaged over the reactor anti-neutrino energy spectrum is obtained in agreement with the experimental data. It is shown that the RFMD enables to describe elastic low-energy NN scattering in accordance with low-energy nuclear phenomenology.

nucl-th↗

arXiv1998

Confinement potential in dual Monopole Nambu-Jona-Lasinio model with dual Dirac strings

Interquark confinement potential is calculated in the dual Monopole Nambu-Jona-Lasinio model with dual Dirac strings as a functional of a dual Dirac string length. The calculation is carried out by the explicit integration over quantum fluctuations of a dual-vector field (monopole-antimonopole collective excitation) around the Abrikosov flux line and string shape fluctuations. The contribution of the scalar field (monopole-antimonopole collective excitation) exchange is taken into account in the tree approximation due to the London limit regime.

hep-th↗

arXiv1998

Center Projection With and Without Gauge Fixing

We consider projections of SU(2) lattice link variables onto Z(2) center and U(1) subgroups, with and without gauge-fixing. It is shown that in the absence of gauge-fixing, and up to an additive constant, the static quark potential extracted from projected variables agrees exactly with the static quark potential taken from the full link variables; this is an extension of recent arguments by Ambjorn and Greensite, and by Ogilvie. Abelian and center dominance is essentially trivial in this case, and seems of no physical relevance. The situation changes drastically upon gauge fixing. In the case of center projection, there are a series of tests one can carry out, to check if vortices identified in the projected configurations are physical objects. All these criteria are satisfied in maximal center gauge, and we show here that they all fail in the absence of gauge fixing. The non-triviality of center projection is due entirely to the maximal center gauge-fixing, which pumps information about the location of extended physical objects into local Z(2) observables.

hep-lat↗

arXiv1998

Asymptotic Scaling, Casimir Scaling, and Center Vortices

We report on two recent developments in the center vortex theory of confinement: (i) the asymptotic scaling of the vortex density, as measured in Monte Carlo simulations; and (ii) an explanation of Casimir scaling and the adjoint string tension, in terms of the center vortex mechanism.

hep-lat↗

arXiv1998

Evidence for a Center Vortex Origin of the Adjoint String Tension

Wilson loops in the adjoint representation are evaluated on cooled lattices in SU(2) lattice gauge theory. It is found that the string tension of an adjoint Wilson loop vanishes, if the loop is evaluated in a sub-ensemble of configurations in which no center vortex links the loop. This result supports our recent proposal that the adjoint string tension, in the Casimir-scaling regime, can be attributed to a center vortex mechanism.

hep-lat↗

arXiv1998

Quantum and string shape fluctuations in the dual Monopole Nambu-Jona-Lasinio model with dual Dirac strings

The magnetic monopole condensate is calculated in the dual Monopole Nambu-Jona-Lasinio model with dual Dirac strings suggested in Refs.[1,2] as a functional of the dual Dirac string shape. The calculation is carried out in the tree approximation in the scalar monopole-antimonopole collective excitation field. The integration over quantum fluctuations of the dual-vector monopole-antimonopole collective excitation field around the Abrikosov flux line and string shape fluctuations are performed explicitly. We claim that there are important contributions of quantum and string shape fluctuations to the magnetic monopole condensate.

hep-th↗

arXiv1998

Center dominance, Casimir scaling, and confinement in lattice gauge theory

We present numerical evidence that supports the theory of quark confinement based on center vortex condensation. We introduce a special gauge ("maximal center gauge") and center projection, suitable for identification of center vortices. Main focus is then put on the connection of vortices in center projection to "confiners" in full, unprojected gauge-field configurations. Topics briefly discussed include: the relation between vortices and monopoles, first results for SU(3), and the problem of Casimir scaling.

hep-lat↗

arXiv1998

Nambu-Jona-Lasinio approach to realization of confining medium

The mechanism of a confining medium is investigated within the Nambu-Jona-Lasinio (NJL) approach. It is shown that a confining medium can be realized in the bosonized phase of the NJL model due to vacuum fluctuations of both fermion and Higgs (scalar fermion-antifermion collective excitation) fields. In such an approach there is no need to introduce Dirac strings.

hep-th↗

arXiv1998

Detection of Center Vortices in the Lattice Yang-Mills Vacuum

We discuss the implementation of the ``direct'' maximal center gauge (a gauge which maximizes the lattice average of the squared-modulus of the trace of link variables), and its use in identifying Z(2) center vortices in Yang-Mills vacuum configurations generated by lattice Monte Carlo. We find that center vortices identified in the vacuum state account for the full asymptotic string tension. Scaling of vortex densities with lattice coupling, change in vortex size with cooling, and sensitivity to Gribov copies is discussed. Preliminary evidence is presented, on small lattices, for center dominance in SU(3) lattice gauge theory.

hep-lat↗

arXiv1997

Casimir Scaling from Center Vortices: Towards an Understanding of the Adjoint String Tension

We argue that the approximate ``Casimir scaling'' of the string tensions of higher-representation Wilson loops is an effect due to the finite thickness of center vortex configurations. It is shown, in the context of a simple model of the Z(2) vortex core, how vortex condensation in Yang-Mills theory can account for both Casimir scaling in intermediate size loops, and color-screening in larger loops. An implication of our model is that the deviations from exact Casimir scaling, which tend to grow with loop size, become much more pronounced as the dimensionality of the group representation increases.

hep-lat↗

arXiv1997

Towards the Deconfinement Phase Transition in Hot Gauge Theories

The phase structure of hot gauge theories with dynamical matter fields is reexamined in the canonical ensemble with respect to triality. We discuss properties of chromoelectric and chromomagnetic sectors of the theory and show whereas electric charges carrying a unit of Z(N) charge are screened at high temperatures via dynamical matter loops, this is not the case for the Z(N) magnetic flux. An order parameter is constructed to probe the realization of local Z(N) symmetry in the magnetic sector. We argue this order parameter may be used to detect the deconfinement phase transition which is defined in terms of the screening mechanism.

hep-lat↗

arXiv1997

On the relativistic field theory model of the deuteron II

The relativistic field theory model of the deuteron is applied to the calculation of the cross sections of the low-energy radiative neutron-proton capture n + p -> D + gamma and the low-energy two-proton fusion p + p -> D + e^+ + nu_e. For the low-energy radiative neutron-proton capture n + p -> D + gamma our result agrees well with both the experimental data and the potential model prediction. In the case of the two-proton fusion the cross section obtained is 2.9 times as much as that given by the potential approach. The obtained result is discussed in connection with the solar neutrino problem. ERRATUM: We correct the value of the cross section for pp-fusion p + p -> D + e^+ + nu_e. We find a contribution to the astrophysical factor δS_pp(0) = 2.01 x 10^{-25} (1 +/- 0.30) MeV b which is obtained only due to weak and strong low-energy interactions of the protons and the deuteron when neglecting the Coulomb repulsion between protons in the intermediate state. Minor misprints are corrected.

nucl-th↗

arXiv1997

Center Vortices and the Asymptotic String Tension

We present a method for locating center vortices (``fluxons'') in thermalized lattice gauge field configurations. We find evidence, in lattice Monte Carlo simulations, that the asymptotic string tension of fundamental-representation Wilson loops is due to fluctuations in the number of center vortices linking those loops.

hep-lat↗

arXiv1997

Center Dominance, Center Vortices, and Confinement

We present a variety of numerical data supporting the Center Vortex theory of confinement. A method is introduced for identifying the location of center vortices, in thermalized gauge-field configurations generated by lattice Monte Carlo. Fluctuations in the number of such vortices, linked to fundamental representation Wilson loops, appear to be responsible for the asymptotic string tension extracted from those loops.

hep-lat↗