18 research outputs found
Chern-Simons term in the 4-dimensional SU(2) Higgs Model
Using Seiberg's definition for the geometric charge in SU(2) lattice gauge
theory, we have managed to apply it also to the Chern-Simons term. We checked
the periodic structure and determined the Chern-Simons density on small
lattices and with L=4,\, 6,\mbox{ and }8 near the
critical region in the SU(2) Higgs model. The data indicate that tunneling is
increased at high temperature.Comment: 7 pages plus 4 PS figure
Vacuum Tunneling and Periodic Structure in Lattice Higgs Models
Using a geometric definition for the lattice Chern-Simons term in even
dimensions, we have studied the distribution of Chern-Simons numbers for the
2d-U(1) and the 4d-SU(2) lattice Higgs models. The periodic structure of the
distributions is preserved in our lattice formulation and has been examined in
detail. In both cases the finite size effects visible in the distribution of
Chern-Simons numbers are well accounted for by the Haar measure. Moreover, we
find that grows with the spatial volume. We also
find numerical evidence that tunneling in 4d is increased at high temperature.
(PS-File including Figures available via E-mail: [email protected])Comment: 25 pages, 5 figures, LaTeX (+ PicLaTeX) file, HLRZ-93-08 and BI-TP
93/0
Multigrid Monte Carlo Algorithms for SU(2) Lattice Gauge Theory: Two versus Four Dimensions
We study a multigrid method for nonabelian lattice gauge theory, the time
slice blocking, in two and four dimensions. For SU(2) gauge fields in two
dimensions, critical slowing down is almost completely eliminated by this
method. This result is in accordance with theoretical arguments based on the
analysis of the scale dependence of acceptance rates for nonlocal Metropolis
updates. The generalization of the time slice blocking to SU(2) in four
dimensions is investigated analytically and by numerical simulations. Compared
to two dimensions, the local disorder in the four dimensional gauge field leads
to kinematical problems.Comment: 24 pages, PostScript file (compressed and uuencoded), preprint
MS-TPI-94-
Spin glass overlap barriers in three and four dimensions
For the Edwards-Anderson Ising spin-glass model in three and four dimensions
(3d and 4d) we have performed high statistics Monte Carlo calculations of those
free-energy barriers which are visible in the probability density
of the Parisi overlap parameter . The calculations rely on the
recently introduced multi-overlap algorithm. In both dimensions, within the
limits of lattice sizes investigated, these barriers are found to be
non-self-averaging and the same is true for the autocorrelation times of our
algorithm. Further, we present evidence that barriers hidden in dominate
the canonical autocorrelation times.Comment: 20 pages, Latex, 12 Postscript figures, revised version to appear in
Phys. Rev.
Numerical simulations of a non-commutative theory: the scalar model on the fuzzy sphere
We address a detailed non-perturbative numerical study of the scalar theory
on the fuzzy sphere. We use a novel algorithm which strongly reduces the
correlation problems in the matrix update process, and allows the investigation
of different regimes of the model in a precise and reliable way. We study the
modes associated to different momenta and the role they play in the ``striped
phase'', pointing out a consistent interpretation which is corroborated by our
data, and which sheds further light on the results obtained in some previous
works. Next, we test a quantitative, non-trivial theoretical prediction for
this model, which has been formulated in the literature: The existence of an
eigenvalue sector characterised by a precise probability density, and the
emergence of the phase transition associated with the opening of a gap around
the origin in the eigenvalue distribution. The theoretical predictions are
confirmed by our numerical results. Finally, we propose a possible method to
detect numerically the non-commutative anomaly predicted in a one-loop
perturbative analysis of the model, which is expected to induce a distortion of
the dispersion relation on the fuzzy sphere.Comment: 1+36 pages, 18 figures; v2: 1+55 pages, 38 figures: added the study
of the eigenvalue distribution, added figures, tables and references, typos
corrected; v3: 1+20 pages, 10 eps figures, new results, plots and references
added, technical details about the tests at small matrix size skipped,
version published in JHE
Monopole characteristics in various Abelian gauges
Renormalization group (RG) smoothing is employed on the lattice to
investigate and to compare the monopole structure of the SU(2) vacuum as seen
in different gauges (maximally Abelian (MAG), Polyakov loop (PG) and Laplacian
gauge (LG)). Physically relevant types of monopoles (LG and MAG) are
distinguished by their behavior near the deconfining phase transition. For the
LG, Abelian projection reproduces well the gauge independent monopole structure
encoded in an auxiliary Higgs field. Density and localization properties of
monopoles, their non-Abelian action and topological charge are studied. Results
are presented confirming the Abelian dominance with respect to the
non-perturbative static potential for all gauges considered.Comment: 36 pages, 12 figure
Supersymmetric Regularization, Two-Loop QCD Amplitudes and Coupling Shifts
We present a definition of the four-dimensional helicity (FDH) regularization
scheme valid for two or more loops. This scheme was previously defined and
utilized at one loop. It amounts to a variation on the standard 't
Hooft-Veltman scheme and is designed to be compatible with the use of helicity
states for "observed" particles. It is similar to dimensional reduction in that
it maintains an equal number of bosonic and fermionic states, as required for
preserving supersymmetry. Supersymmetry Ward identities relate different
helicity amplitudes in supersymmetric theories. As a check that the FDH scheme
preserves supersymmetry, at least through two loops, we explicitly verify a
number of these identities for gluon-gluon scattering (gg to gg) in
supersymmetric QCD. These results also cross-check recent non-trivial two-loop
calculations in ordinary QCD. Finally, we compute the two-loop shift between
the FDH coupling and the standard MS-bar coupling, alpha_s. The FDH shift is
identical to the one for dimensional reduction. The two-loop coupling shifts
are then used to obtain the three-loop QCD beta function in the FDH and
dimensional reduction schemes.Comment: 44 pages, minor corrections and clarifications include