Thu·Nov 24, 2005Thursday·November 24, 2005

1. 01*

   Scaling Properties of the Probability Distribution of Lattice Gribov Copies

   A.Y. Lokhov🇫🇷 · O. Pène🇫🇷 · C. Roiesnel🇫🇷

   We study the problem of the Landau gauge fixing in the case of the SU(2) lattice gauge theory. We show that the probability to find a lattice Gribov copy increases considerably when the physical size of the lattice exceeds some critical value $\approx 2.75/\sqrt{\sigma }$, almost independent of the lattice spacing. The impact of the choice of the copy on Green functions is presented. We confirm that the ghost propagator depends on the choice of the copy, this dependence decreasing for increasing volumes above the critical one. The gluon propagator as well as the gluonic three-point functions are insensitive to choice of the copy (within present statistical errors). Finally we show that gauge copies which have the same value of the minimisation functional ($\int d^{4}x(A_{\mu }^a{)}^2$) are equivalent, up to a global gauge transformation, and yield the same Green functions.

   hep-lathep-ph6 citations
2. 02*

   SU(2) Gluodynamics and HP1 sigma-model embedding: Scaling, Topology and Confinement

   P.Yu.Boyko🇷🇺 · F.V.Gubarev🇷🇺 · S.M.Morozov🇷🇺

   We investigate recently proposed HP1 sigma-model embedding method aimed to study the topology of SU(2) gauge fields. The HP1 based topological charge is shown to be fairly compatible with various known definitions. We study the corresponding topological susceptibility and estimate its value in the continuum limit. The geometrical clarity of HP1 approach allows to investigate non-perturbative aspects of SU(2) gauge theory on qualitatively new level. In particular, we obtain numerically precise estimation of gluon condensate and its leading quadratic correction. Furthermore, we present clear evidences that the string tension is to be associated with global (percolating) regions of sign-coherent topological charge. As a byproduct of our analysis we estimate the continuum value of quenched chiral condensate and the dimensionality of regions, which localize the lowest eigenmodes of overlap Dirac operator.

   hep-lathep-phPRD(2006)·13 citations
3. 03*

   Overlap Hypercube Fermions in QCD

   W. Bietenholz🇩🇪 · S. Shcheredin🇩🇪

   We present simulation results obtained with overlap hypercube fermions in QCD near the chiral limit. We relate our results to chiral perturbation theory in both, the epsilon-regime and in the p-regime. In particular we measured the pion decay constant by different methods, as well as the chiral condensate, light meson masses, the PCAC quark mass and the renormalisation constant Z_A.

   hep-latNucl.Phys.B Proc.Suppl.(2006)·3 citations
4. 04*

   Fun with Dirac eigenvalues

   Michael Creutz🇺🇸

   It is popular to discuss low energy physics in lattice gauge theory in terms of the small eigenvalues of the lattice Dirac operator. I play with some ensuing pitfalls in the interpretation of these eigenvalue spectra.

   hep-lat13 citations
5. 05*

   Landau gauge ghost and gluon propagators and the Faddeev-Popov operator spectrum

   A. Sternbeck🇩🇪 · E.-M. Ilgenfritz🇩🇪 · M. Müller-Preussker (Humboldt-Universität zu Berlin)🇩🇪 · A. Schiller (Universität Leipzig)🇩🇪

   In this talk we report on a recent lattice investigation of the Landau gauge gluon and ghost propagators in pure SU(3) lattice gauge theory with a special emphasis on the Gribov copy problem. In the (infrared) region of momenta $q^2\le 0.3{\mathrm{GeV}}^2$ we find the corresponding MOM scheme running coupling ${\alpha }_s(q^2)$ to rise in $q$. We also report on a first SU(3) computation of the ghost-gluon vertex function showing that it deviates only weakly from being constant. In addition we study the spectrum of low-lying eigenvalues and eigenfunctions of the Faddeev-Popov operator as well as the spectral representation of the ghost propagator.

   hep-latNucl.Phys.B Proc.Suppl.(2006)·23 citations
6. 06*

   Generalized dual symmetry of nonabelian theories and the freezing of \alpha_s

   C.R. Das🇮🇳 · L.V. Laperashvili🇷🇺 · H.B. Nielsen🇩🇰

   The quantum Yang-Mills theory, describing a system of fields with non-dual (chromo-electric g) and dual (chromo-magnetic \tilde g) charges and revealing the generalized dual symmetry, is developed by analogy with the Zwanziger formalism in QED. The renormalization group equations (RGEs) for pure nonabelian theories are analysed for both constants, \alpha = g^2 / 4\pi and \tilde\alpha = {\tilde g}^2 / 4\pi. The pure SU(3) \times \widetilde{SU(3)} gauge theory is investigated as an example. We consider not only monopoles, but also dyons. The behaviour of the total SU(3) \beta-function is investigated in the whole region of \alpha \equiv \alpha_s: 0 \le \alpha < \infty. It is shown that this \beta-function is antisymmetric under the interchange \alpha \longleftrightarrow 1/\alpha and is given by the well-known perturbative expansion not only for \alpha \ll 1, but also for \alpha \gg 1. Using an idea of the Maximal Abelian Projection by t' Hooft, we considered the formation of strings - the ANO flux tubes - in the Higgs model of scalar monopole (or dyon) fields. In this model we have constructed the behaviour of the \beta-function in the vicinity of the point \alpha = 1, where it acquires a zero value. Considering the phase transition points at \alpha \approx 0.4 and \alpha \approx 2.5, we give the explanation of the freezing of \alpha_s. The evolution of \alpha_s^{-1}(\mu) and the behaviour of V_{eff}(\mu) are investigated for both, perturbative and non-perturbative regions of QCD. It was shown that the effective potential has a minimum, ensured by the dual sector of QCD. The gluon condensate F^2_0, corresponding to this minimum, is predicted: F^2_0 \approx 0.15 GeV^4, in agreement with the well-known results.

   ↳ hep-phhep-lathep-thInt.J.Mod.Phys.A(2006)·6 citations

* Reconstructed cohort: no mailing for this day survives in the archive. Papers are grouped by their submission times and arXiv's announcement cut-off, assuming announcement without delay; positions follow identifier order. Validated at ~91% exact-day agreement against the archived era.