Three Dimensional Nonlinear Sigma Models in the Wilsonian Renormalization Method

The three dimensional nonlinear sigma model is unrenormalizable in perturbative method. By using the $\beta$ function in the nonperturbative Wilsonian renormalization group method, we argue that ${\cal N}=2$ supersymmetric nonlinear $\sigma$ models are renormalizable in three dimensions. When the target space is an Einstein-K\"{a}hler manifold with positive scalar curvature, such as C$P^N$ or $Q^N$, there are nontrivial ultraviolet (UV) fixed point, which can be used to define the nontrivial continuum theory. If the target space has a negative scalar curvature, however, the theory has only the infrared Gaussian fixed point, and the sensible continuum theory cannot be defined. We also construct a model which interpolates between the C$P^N$ and $Q^N$ models with two coupling constants. This model has two non-trivial UV fixed points which can be used to define the continuum theory. Finally, we construct a class of conformal field theories with ${\bf SU}(N)$ symmetry, defined at the fixed point of the nonperturbative $\beta$ function. These conformal field theories have a free parameter corresponding to the anomalous dimension of the scalar fields. If we choose a specific value of the parameter, we recover the conformal field theory defined at the UV fixed point of C$P^N$ model and the symmetry is enhanced to ${\bf SU}(N+1)$.Comment: 16 pages, 1 figure, references adde

Unitarity Bound of the Wave Function Renormalization Constant

The wave function renormalization constant $Z$, the probability to find the bare particle in the physical particle, usually satisfies the unitarity bound $0 \leq Z \leq 1$ in field theories without negative metric states. This unitarity bound implies the positivity of the anomalous dimension of the field in the one-loop approximation. In nonlinear sigma models, however, this bound is apparently broken because of the field dependence of the canonical momentum. The contribution of the bubble diagrams to the anomalous dimension can be negative, while the contributions from more than two particle states satisfies the positivity of the anomalous dimension as expected. We derive the genuine unitarity bound of the wave function renormalization constant.Comment: 8 pages, 2 figures, comments adde

Normal Coordinates in Kahler Manifolds and the Background Field Method

Riemann normal coordinates (RNC) are unsuitable for Kahler manifolds since they are not holomorphic. Instead, Kahler normal coordinates (KNC) can be defined as holomorphic coordinates. We prove that KNC transform as a holomorphic tangent vector under holomorphic coordinate transformations, and therefore they are natural extensions of RNC to the case of Kahler manifolds. The KNC expansion provides the manifestly covariant background field method preserving the complex structure in supersymmetric nonlinear sigma models

Technicolor Models with Color-Singlet Technifermions and their Ultraviolet Extensions

We study technicolor models in which all of the technifermions are color-singlets, focusing on the case in these fermions transform according to the fundamental representation of the technicolor gauge group. Our analysis includes a derivation of restrictions on the weak hypercharge assignments for the technifermions and additional color-singlet, technisinglet fermions arising from the necessity of avoiding stable bound states with exotic electric charges. Precision electroweak constraints on these models are also discussed. We determine some general properties of extended technicolor theories containing these technicolor sectors.Comment: 17 pages, latex, 2 figure

Direct observation of localization in the minority-spin-band electrons of magnetite below the Verwey temperature

Two-dimensional spin-uncompensated momentum density distributions, $\rho_{\rm s}^{2D}({\bf p})$s, were reconstructed in magnetite at 12K and 300K from several measured directional magnetic Compton profiles. Mechanical de-twinning was used to overcome severe twinning in the single crystal sample below the Verwey transition. The reconstructed $\rho_{\rm s}^{2D}({\bf p})$ in the first Brillouin zone changes from being negative at 300 K to positive at 12 K. This result provides the first clear evidence that electrons with low momenta in the minority spin bands in magnetite are localized below the Verwey transition temperature.Comment: 13 pages, 4 figures, accepted in Physical Review

Basic Consideration on EAF Dust Treatment Using Hydrometallurgical Processes

Electric Arc Furnace (EAF) dust, defined as special industrial waste in Japan, is treated through pyrometallurgical processes in which crude ZnO powder is recovered. An on-site type process, however, is desired to reduce treatment cost and cost of transportation of the dust. A hydrometallurgical process is considered to be suitable for such an on-site treatment. Although many EAF dust treatment processes by hydrometallurgical method have been proposed, most of them have not been commercialized in Japan. A short review of hydrometallurgical processes foe EAF dust was done and a new hydrometallurgical process for EAF dust was proposed in this study. Nitric acid solution is used for the extraction of ZnO from the dust. Some characteristics of the process are as follows: 1. Recovery of Zn from zinc ferrite in EAF dust is the target, while the dissolution of Fe is limited by controlling the pH of the solution. 2. Zn is recovered as metallic Zn by electrowinning from the solution and nitric acid is regenerated in the anode.報文Original Pape

A High-Resolution Compton Scattering Study of the Electron Momentum Density in Al

We report high-resolution Compton profiles (CP's) of Al along the three principal symmetry directions at a photon energy of 59.38 keV, together with corresponding highly accurate theoretical profiles obtained within the local-density approximation (LDA) based band-theory framework. A good accord between theory and experiment is found with respect to the overall shapes of the CP's, their first and second derivatives, as well as the anisotropies in the CP's defined as differences between pairs of various CP's. There are however discrepancies in that, in comparison to the LDA predictions, the measured profiles are lower at low momenta, show a Fermi cutoff which is broader, and display a tail which is higher at momenta above the Fermi momentum. A number of simple model calculations are carried out in order to gain insight into the nature of the underlying 3D momentum density in Al, and the role of the Fermi surface in inducing fine structure in the CP's. The present results when compared with those on Li show clearly that the size of discrepancies between theoretical and experimental CP's is markedly smaller in Al than in Li. This indicates that, with increasing electron density, the conventional picture of the electron gas becomes more representative of the momentum density and that shortcomings of the LDA framework in describing the electron correlation effects become less important.Comment: 7 pages, 6 figures, regular articl

Role of Oxygen Electrons in the Metal-Insulator Transition in the Magnetoresistive Oxide La2−2x_{2-2x}Sr1+2x_{1+2x}Mn2_2O7_7 Probed by Compton Scattering

We have studied the [100]-[110] anisotropy of the Compton profile in the bilayer manganite. Quantitative agreement is found between theory and experiment with respect to the anisotropy in the two metallic phases (i.e. the low temperature ferromagnetic and the colossal magnetoresistant phase under a magnetic field of 7 T). Robust signatures of the metal-insulator transition are identified in the momentum density for the paramagnetic phase above the Curie temperature. We interpret our results as providing direct evidence for the transition from the metallic-like to the admixed ionic-covalent bonding accompanying the magnetic transition. The number of electrons involved in this phase transition is estimated from the area enclosed by the Compton profile anisotropy differences. Our study demonstrates the sensitivity of the Compton scattering technique for identifying the number and type of electrons involved in the metal-insulator transition.Comment: 4 pages, 4 figures, accepted for publication in Physical Review Letter

Lattice Simulations and Infrared Conformality

We examine several recent lattice-simulation data sets, asking whether they are consistent with infrared conformality. We observe, in particular, that for an SU(3) gauge theory with 12 Dirac fermions in the fundamental representation, recent simulation data can be described assuming infrared conformality. Lattice simulations include a fermion mass m which is then extrapolated to zero, and we note that this data can be fit by a small-m expansion, allowing a controlled extrapolation. We also note that the conformal hypothesis does not work well for two theories that are known or expected to be confining and chirally broken, and that it does work well for another theory expected to be infrared conformal.Comment: 6 pages, 4 figures. v2: added new fit including finite-volume corrections. v3: updated to match published versio

Bulk Fermi surface and momentum density in heavily doped La2−x_{2-x}Srx_xCuO4_4 using high resolution Compton scattering and positron annihilation spectroscopies

We have observed the bulk Fermi surface (FS) in an overdoped ($x$=0.3) single crystal of La$_{2-x}$Sr$_x$CuO$_4$ by using Compton scattering. A two-dimensional (2D) momentum density reconstruction from measured Compton profiles yields a clear FS signature in the third Brillouin zone along [100]. The quantitative agreement between density functional theory (DFT) calculations and momentum density experiment suggests that Fermi-liquid physics is restored in the overdoped regime. In particular the predicted FS topology is found to be in good accord with the corresponding experimental data. We find similar quantitative agreement between the measured 2D angular correlation of positron annihilation radiation (2D-ACAR) spectra and the DFT based computations. However, 2D-ACAR does not give such a clear signature of the FS in the extended momentum space in either the theory or the experiment.Comment: 9 pages, 8 figure