Laplacian modes probing gauge fields

We show that low-lying eigenmodes of the Laplace operator are suitable to represent properties of the underlying SU(2) lattice configurations. We study this for the case of finite temperature background fields, yet in the confinement phase. For calorons as classical solutions put on the lattice, the lowest mode localizes one of the constituent monopoles by a maximum and the other one by a minimum, respectively. We introduce adjustable phase boundary conditions in the time direction, under which the role of the monopoles in the mode localization is interchanged. Similar hopping phenomena are observed for thermalized configurations. We also investigate periodic and antiperiodic modes of the adjoint Laplacian for comparison. In the second part we introduce a new Fourier-like low-pass filter method. It provides link variables by truncating a sum involving the Laplacian eigenmodes. The filter not only reproduces classical structures, but also preserves the confining potential for thermalized ensembles. We give a first characterization of the structures emerging from this procedure.Comment: 43 pages, 26 figure

Modelling photometric reverberation data -- a disk-like broad-line region and a potentially larger black hole mass for 3C120

We consider photometric reverberation mapping, where the nuclear continuum variations are monitored via a broad-band filter and the echo of emission line clouds of the broad line region (BLR) is measured with a suitable narrow-band (NB) filter. We investigate how an incomplete emission-line coverage by the NB filter influences the BLR size determination. This includes two basic cases: 1) a symmetric cut of the blue and red part of the line wings, and 2) the filter positioned asymmetrically to the line centre so that essentially a complete half of the emission line is contained in the NB filter. Under the assumption that the BLR size is dominated by circular Keplerian orbits, we find that symmetric cutting of line wings may lead to overestimating the BLR size by less than 5%. The case of asymmetric half-line coverage, similar as for our data of the Seyfert 1 galaxy 3C120, yields the BLR size with a bias of less than 1%. Our results suggest that any BLR size bias due to narrow-band line cut in photometric reverberation mapping is small and in most cases negligible. We used well sampled photometric reverberation mapping light curves with sharp variation features in both the continuum and the Hbeta light curves to determine the geometry type of the Hbeta BLR for 3C120. Modelling of the light curve, under the assumption that the BLR is essentially virialised, argues against a spherical geometry and favours a nearly face-on disk-like geometry with inclination i = 10 +/- 4 deg and extension from 22 to 28 light days. The low inclination may lead to a larger black hole mass than the derived when using the average geometry scaling factor f=5.5. We discuss deviations of Seyfert 1 galaxies from the M_BH - sigma relation.Comment: 9 pages, 11 figures, accepted for publication in Astronomy and Astrophysic

Probing for Instanton Quarks with epsilon-Cooling

We use epsilon-cooling, adjusting at will the order a^2 corrections to the lattice action, to study the parameter space of instantons in the background of non-trivial holonomy and to determine the presence and nature of constituents with fractional topological charge at finite and zero temperature for SU(2). As an additional tool, zero temperature configurations were generated from those at finite temperature with well-separated constituents. This is achieved by "adiabatically" adjusting the anisotropic coupling used to implement finite temperature on a symmetric lattice. The action and topological charge density, as well as the Polyakov loop and chiral zero-modes are used to analyse these configurations. We also show how cooling histories themselves can reveal the presence of constituents with fractional topological charge. We comment on the interpretation of recent fermion zero-mode studies for thermalized ensembles at small temperatures.Comment: 26 pages, 14 figures in 33 part

Monopole and vortex content of a meron pair

We investigate the monopole and vortex content of a meron pair by calculating the points at which the transformation to the Laplacian Center Gauge is ill-defined and by studying the behavior of Wilson loops. These techniques reveal complementary aspects of the vortex and monopole structure, including the presence of closed monopole lines and closed vortex surfaces joining the two merons, and evidence for intersecting vortex surfaces at each meron.Comment: 14 pages, 5 figures. v2, minor changes, references added, to appear in PL

Adjoint quarks and fermionic boundary conditions

We study quenched SU(2) lattice gauge theory with adjoint fermions in a wide range of temperatures. We focus on spectral quantities of the Dirac operator and use the temporal fermionic boundary conditions as a tool to probe the system. We determine the deconfinement temperature through the Polyakov loop, and the chiral symmetry restoration temperature for adjoint fermions through the gap in the Dirac spectrum. This chiral transition temperature is about four times larger than the deconfinement temperature. In between the two transitions we find that the system is characterized by a non-vanishing chiral condensate which differs for periodic and anti-periodic fermion boundary conditions. Only for the latter (physical) boundary conditions, the condensate vanishes at the chiral transition. The behavior between the two transitions suggests that deconfinement manifests itself as the onset of a dependence of spectral quantities of the Dirac operator on boundary conditions. This picture is supported further by our results for the dual chiral condensate.Comment: Minor changes; final version to appear in JHE

The history of Shtokman field development

Let's twist again! The first highly enantioselective asymmetric reaction in which a chiral reaction medium is the sole source of chirality is presented. The aza‐Baylis–Hillman reaction in an ionic liquid with a chiral anion, whose design is based on mechanistic insights, gave products with up to 84 % ee

Numerical properties of staggered quarks with a taste-dependent mass term

The numerical properties of staggered Dirac operators with a taste-dependent mass term proposed by Adams [1,2] and by Hoelbling [3] are compared with those of ordinary staggered and Wilson Dirac operators. In the free limit and on (quenched) interacting configurations, we consider their topological properties, their spectrum, and the resulting pion mass. Although we also consider the spectral structure, topological properties, locality, and computational cost of an overlap operator with a staggered kernel, we call attention to the possibility of using the Adams and Hoelbling operators without the overlap construction. In particular, the Hoelbling operator could be used to simulate two degenerate flavors without additive mass renormalization, and thus without fine-tuning in the chiral limit.Comment: 14 pages, 9 figures. V2: published version; important note added regarding Hoelbling fermions, otherwise minor change

Chiral and deconfinement transition from correlation functions: SU(2) vs. SU(3)

We study a gauge invariant order parameter for deconfinement and the chiral condensate in SU(2) and SU(3) Yang-Mills theory in the vicinity of the deconfinement phase transition using the Landau gauge quark and gluon propagators. We determine the gluon propagator from lattice calculations and the quark propagator from its Dyson-Schwinger equation, using the gluon propagator as input. The critical temperature and a deconfinement order parameter are extracted from the gluon propagator and from the dependency of the quark propagator on the temporal boundary conditions. The chiral transition is determined using the quark condensate as order parameter. We investigate whether and how a difference in the chiral and deconfinement transition between SU(2) and SU(3) is manifest.Comment: 15 pages, 9 figures. For clarification one paragraph and two references added in the introduction and two sentences at the end of the first and last paragraph of the summary. Appeared in EPJ

Confinement, Chiral Symmetry Breaking, and Axial Anomaly from Domain Formation at Intermediate Resolution

Based on general renormalization group arguments, Polyakov's loop-space formalism, and recent analytical lattice arguments, suggesting, after Abelian gauge fixing, a description of pure gluodynamics by means of a Georgi-Glashow like model, the corresponding vacuum fields are defined in a non-local way. Using lattice information on the gauge invariant field strength correlator in full QCD, the resolution scale \La_b, at which these fields become relevant in the vacuum, is determined. For SU(3) gauge theory it is found that \La_b\sim 2.4 GeV, 3.1 GeV, and 4.2 GeV for ($N_F=4, m_q=18$ MeV), ($N_F=4, m_q=36$ MeV), and pure gluodynamics, repectively. Implications for the operator product expansion of physical correlators are discussed. It is argued that the emergence of magnetic (anti)monopoles in the vacuum at resolution \La_b is a direct consequence of the randomness in the formation of a low entropy Higgs condensate. This implies a breaking of chiral symmetry and a proliferation of the axial U(1) anomaly at this scale already. Justifying Abelian projection, a decoupling of non-Abelian gauge field fluctuations from the dynamics occurs. The condensation of (anti)monopoles at \La_c<\La_b follows from the demand that vacuum fields ought to have vanishing action at any resolution. As monopoles condense they are reduced to their cores, and hence they become massless. Apparently broken gauge symmetries at resolutions \La_c<\La\le\La_b are restored in this process.Comment: 11 pages, 3 figure