arXiv subjects
Publications and source records attributed to E. -M. Ilgenfritz.
Using the renormalization group based smoothing technique we have studied the gauge invariant field strength correlator at T\ne0 and T=0 in pure SU(2) gauge theory. In conjunction with a cluster analysis, the field strength correlator is used to study correlations between the clusters in space and color orientation.
Numerical data for the SU(2) confining string in the maximal abelian projection are analysed. The distribution of the electric flux and monopole currents are perfectly described by the classical equations of motion for the dual Abelian Higgs model. The mass of the vector boson is equal to the mass of the monopole (Higgs particle) within numerical errors. The classical energy per unit length of the Abrikosov vortex reproduces 94% of the full non-Abelian string tension.
Local correlations of Z-vortex operators with gauge and Higgs fields (lattice quantum vortex profiles) as well as vortex two-point functions are studied in the crossover region near a Higgs mass of 100 GeV within the 3D SU(2) Higgs model. The vortex profiles resemble certain features of the classical vortex solutions in the continuum. The vortex-vortex interactions are analogous to the interactions of Abrikosov vortices in a type-I superconductor.
We study the improvement of simulations of QCD with dynamical Wilson fermions by combining the Hybrid Monte Carlo algorithm with parallel tempering. As an indicator for decorrelation we use the topological charge.
We summarize recent attempts to extract characteristics of non-perturbative vacuum structure from lattice measurements of the gauge invariant field strength correlator. As an alternative to cooling, we propose to apply the renormalization group (RG) smoothing method in lattice studies. For pure SU(2) gauge theory we present magnetic and electric correlation lengths and condensates related to various correlators over a temperature range of 0.7 T_{dec} < T < 1.9 T_{dec}
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.
Embedded defects proposed long ago (Z-vortices and Nambu monopoles) have been successfully searched for in 3D equilibrium lattice studies within the standard model near the electroweak phase transition and the crossover (which follows it for realistic Higgs mass). Gauge independent lattice-vortex operators are proposed. Vortex condensation (percolation) is found to characterize the high-temperature phase. Small vortex clusters are thermally activated with non-negligible density on the low-temperature side only at higher Higgs mass, where preliminary evidence supports their semiclassical nature.
Finite temperature SU(2) lattice gauge theory is investigated in a 3D cubic box with fixed boundary conditions provided by a discretized, static BPS monopole solution with varying core scale $μ$. Using heating and cooling techniques we establish that for discrete $μ$-values stable classical solutions either of self-dual or of pure magnetic type exist inside the box. Having switched on quantum fluctuations we compute the Polyakov line and other local operators. For different $μ$ and at varying temperatures near the deconfinement transition we study the influence of the boundary condition on the vacuum inside the box. In contrast to the pure magnetic background field case, for the self-dual one we observe confinement even for temperatures quite far above the critical one.
Finite temperature SU(2) lattice gauge theory is investigated in a 3D cubic box with fixed boundary conditions (b.c.) provided by a discretized, static BPS monopole solution with varying core scale $μ$. For discrete $μ$-values we find stable classical solutions either of electro-magnetic ('dyon') or of purely magnetic type inside the box. Near the deconfinement transition we study the influence of the b.c. on the quantized fields inside the box. In contrast to the purely magnetic background field case, for the dyon case we observe confinement for temperatures above the usual critical one.
We study the statistical properties of Z-vortices and Nambu monopoles in the 3D SU(2) Higgs model for a Higgs mass M_H \approx 100 GeV near and above the crossover temperature, where these defects are thermally excited. Although there is no phase transition at that strong selfcoupling, we observe that the Z-vortices exhibit the percolation transition that has been found recently to accompany the first order thermal transition that exists at smaller Higgs mass. Above the crossover temperature percolating networks of Z-vortex lines are ubiquitous, whereas vortices form a dilute gas of closed vortex loops and (Nambu) monopolium states on the low-temperature side of the crossover. The percolation temperature turns out to be roughly independent of the lattice spacing. We find that the Higgs modulus is smaller (the gauge action is larger) inside the vortices, compared to the bulk average. This correlation becomes very strong on the low-temperature side. The percolation transition is a prerequisite of some string mediated baryon number generation scenarios.
Using the renormalization group motivated smoothing technique we study the semiclassical structure of the pure Yang-Mills vacuum. We carefully check that identified clusters of topological charge behave like instantons around their centers. Looking at distance distributions of clusters we find instanton-antiinstanton pair formation in the deconfined phase. We use suitably normalized gauge invariant field strength correlators to obtain first quantitative information on the relative color orientation of instantons. We give further evidence for a modified instanton profile in the confined phase and present a simple alternative model for it.
We present results for the wave functions and the screening mass spectrum for quantum numbers $0^{++}$, $1^{--}$ and $2^{++}$ in the three-dimensional SU(2)-Higgs model near to the phase transition line below the endpoint and in the crossover region. Varying the 3D gauge couplings we study the behaviour along a line of constant physics towards the continuum limit in both phases. In the crossover region the changing spectrum of screening states versus temperature is examined showing the aftermath of the phase transition at lower Higgs mass. Different to smearing concepts we used large sets of operators with various extensions allowing to identify wave functions in position space.
Using a renormalization group motivated smoothing technique, we investigate the large scale structure of lattice configurations at finite temperature, concentrating on Abelian monopoles identified in the maximally Abelian, the Laplacian Abelian, and the Polyakov gauge. Monopoles are mostly found in regions of large action and topological charge, rather independent of the gauge chosen to detect them. Gauge invariant properties around Abelian monopoles, the local non-Abelian action and topological density, are studied. We show that the local averages of these densities along the monopole trajectories are clearly above the background, which supports the existence of monopoles as physical objects. Characteristic changes of the vacuum structure at the deconfinement transition can be attributed to the corresponding Abelian monopoles, to an extent that depends on the gauge chosen for Abelian projection. All three Abelian projections reproduce the full SU(2) string tension within 10 percent which is preserved by smoothing.
Using the renormalization group motivated smoothing technique, the large scale structure of lattice configurations at finite temperature is characterized in terms of Abelian monopoles identified in the maximally Abelian, the Laplacian Abelian, and the Polyakov gauge. Abundance and anisotropy of monopoles at deconfinement and gauge invariant properties like local non-Abelian action and topological density are studied. Monopoles are predominantly found in regions of large action and topological charge, rather independent of the chosen gauge.
New defects (Z-vortices and Nambu monopoles) are found to become thermodynamically relevant for the broken phase near to the (weakly first order) electroweak phase transition, and below the crossover for higher Higgs mass. The symmetric phase is characterized by vortex condensation (percolation). The percolation transition persists in the crossover region. The quasiclassical nature of the vortices is supported by correlations with Higgs field and gauge field energy. Sphalerons are shown to be related to monopolium bound states.
Wave functions and the screening mass spectrum in the 3D SU(2)-Higgs model near to the phase transition line below the endpoint and in the crossover region are calculated. In the crossover region the changing spectrum versus temperature is examined showing the aftermath of the phase transition at lower Higgs mass. Large sets of operators with various extensions are used allowing to identify wave functions in position space.
Field strength correlators are semi-classically evaluated in the dilute gas model of non-Abelian sources (instantons) and compared with lattice data for QCD at zero temperature. We show that one of the Euclidean invariant, tensorial structures vanishes for configurations being purely selfdual or anti-selfdual. We compute the invariant functions contributing to the correlators within the two lowest orders in an instanton density expansion. Fitting instanton size and density for quenched and full QCD, we obtain a reasonable description.
We study the properties of Nambu monopoles and Z-vortices in the 3D lattice SU(2) Higgs theory which represents the Standard Model at high temperature. We show that the densities of the Nambu monopoles and the Z-vortices are O(1) in the symmetric phase and generically small in the Higgs phase. Near to the critical Higgs mass and in the vicinity of the phase transition the densities are no more negligible in the broken phase. The percolation probability of the Z-vortex lines is found as a new disorder parameter for this phase transition. We conclude that the transition to the symmetric phase is accompanied by Z-vortex condensation. Simulations comparing elementary and extended vortices and monopoles at different β_G values, aiming to show that the density of vortices and monopoles of fixed physical size might have a well-defined continuum limit, gives encouraging but so far inconclusive results.