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 $L^4$ and $L^3 \times 2,\, 4$ 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 $\langle N_{CS}^2 \rangle$ 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 $F^q_B$ which are visible in the probability density $P_J(q)$ of the Parisi overlap parameter $q$. 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 $q$ 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