Vertex Operators in 4D Quantum Gravity Formulated as CFT

We study vertex operators in 4D conformal field theory derived from quantized gravity, whose dynamics is governed by the Wess-Zumino action by Riegert and the Weyl action. Conformal symmetry is equal to diffeomorphism symmetry in the ultraviolet limit, which mixes positive-metric and negative-metric modes of the gravitational field and thus these modes cannot be treated separately in physical operators. In this paper, we construct gravitational vertex operators such as the Ricci scalar, defined as space-time volume integrals of them are invariant under conformal transformations. Short distance singularities of these operator products are computed and it is shown that their coefficients have physically correct sign. Furthermore, we show that conformal algebra holds even in the system perturbed by the cosmological constant vertex operator as in the case of the Liouville theory shown by Curtright and Thorn.Comment: 26 pages, rewrote review part concisely, added explanation

CMB Anisotropies Reveal Quantized Gravity

A novel primordial spectrum with a dynamical scale of quantum gravity origin is proposed to explain the sharp fall off of the angular power spectra at low multipoles in the COBE and WMAP observations. The spectrum is derived from quantum fluctuations of the scalar curvature in a renormalizable model of induced gravity. This model describes the very early universe by the conformal field fluctuating about an inflationary background with the expansion time constant of order of the Planck mass.Comment: 12 pages, 2 figure

Recursion Relations in Liouville Gravity coupled to Ising Model satisfying Fusion Rules

The recursion relations of 2D quantum gravity coupled to the Ising model discussed by the author previously are reexamined. We study the case in which the matter sector satisfies the fusion rules and only the primary operators inside the Kac table contribute. The theory involves unregularized divergences in some of correlators. We obtain the recursion relations which form a closed set among well-defined correlators on sphere, but they do not have a beautiful structure that the bosonized theory has and also give an inconsistent result when they include an ill-defined correlator with the divergence. We solve them and compute the several normalization independent ratios of the well-defined correlators, which agree with the matrix model results.Comment: Latex, 22 page

Koeficijenti udarne ionizacije elektronom i šupljinom u poluvodičima s jakim poljem

We have fitted the soft lucky drift model of impact ionization of Ridley to experimental data for GaAs, InP, Si, Ge and In0.47Ga0.53As semiconductors. Excellent fits of the theory to experimental data were obtained by using least-squares fitting algorithm. A generalized Keldysh formula has been used to introduce a soft threshold factor. Generalized Keldysh formula originates from realistic energy bands in semiconductors at high electric field which reflects the density of states of energy bands. Keldysh factor and a new mean free path are calculated. A comparison with reported values of both Ridley and Marsland showed reasonable agreement for mean free path, but there are still large differences among Keldysh factors.Načinili smo prilagodbe Ridleyvog mekog sretno-posmičnog modela eksperimentalnim podacima za GaAs, InP, Si, Ge i In0.47Ga0.53As. Postigli smo odlično slaganje teorije i eksperimentalnih podataka primjenom metode najmanjih kvadrata. Primijenili smo poopćenu Keldyshevu formulu radi uvođenja mekog faktora praga. Poopćena Keldysheva formula proizlazi iz realnih razmatranja energijskih vrpci u poluvodičima s jakim električnim poljima što odražava gustoću stanja energijskih vrpci. Izračunali smo Keldyshev faktor i nove vrijednosti srednjih slobodnih puteva. Ridleyeve and Marslandove objavljene vrijednosti za srednje slobodne puteve u dobrom su skladu s našima, ali još uvijek nalazimo velike razlike među Keldyshevim faktorima

Quantum Nuclei at Weakly Bonded Interfaces: The Case of Cyclohexane on Rh(111)

The electronic properties of interfaces can depend on their isotopic constitution. One known case is that of cyclohexane physisorbed on Rh(111), in which isotope effects have been measured on the work function change and desorption energies. These effects can only be captured by calculations including nuclear quantum effects (NQE). In this paper, this interface is addressed employing dispersion‐inclusive density‐functional theory coupled to a quasi‐harmonic (QH) approximation for NQE, as well as to fully anharmonic ab initio path integral molecular dynamics (PIMD). The QH approximation is able to capture that deuterated cyclohexane has a smaller adsorption energy and lies about 0.01 Å farther from the Rh(111) surface than its isotopologue, which can be correlated to the isotope effect in the work function change. An investigation of the validity of the QH approximation relying on PIMD simulations, leads to the conclusion that although this interface is highly impacted by anharmonic quantum fluctuations in the molecular layer and at bonding sites, these anharmonic contributions play a minor role when analyzing isotope effects at low temperatures. Nevertheless, anharmonic quantum fluctuations cause an increase in the distance between the molecular layer and Rh(111), a consequent smaller overall work function change, and intricate changes in orbital hybridization

Koeficijenti udarne ionizacije elektronom i šupljinom u poluvodičima s jakim poljem

We have fitted the soft lucky drift model of impact ionization of Ridley to experimental data for GaAs, InP, Si, Ge and In0.47Ga0.53As semiconductors. Excellent fits of the theory to experimental data were obtained by using least-squares fitting algorithm. A generalized Keldysh formula has been used to introduce a soft threshold factor. Generalized Keldysh formula originates from realistic energy bands in semiconductors at high electric field which reflects the density of states of energy bands. Keldysh factor and a new mean free path are calculated. A comparison with reported values of both Ridley and Marsland showed reasonable agreement for mean free path, but there are still large differences among Keldysh factors.Načinili smo prilagodbe Ridleyvog mekog sretno-posmičnog modela eksperimentalnim podacima za GaAs, InP, Si, Ge i In0.47Ga0.53As. Postigli smo odlično slaganje teorije i eksperimentalnih podataka primjenom metode najmanjih kvadrata. Primijenili smo poopćenu Keldyshevu formulu radi uvođenja mekog faktora praga. Poopćena Keldysheva formula proizlazi iz realnih razmatranja energijskih vrpci u poluvodičima s jakim električnim poljima što odražava gustoću stanja energijskih vrpci. Izračunali smo Keldyshev faktor i nove vrijednosti srednjih slobodnih puteva. Ridleyeve and Marslandove objavljene vrijednosti za srednje slobodne puteve u dobrom su skladu s našima, ali još uvijek nalazimo velike razlike među Keldyshevim faktorima

Making a Universe

For understanding the origin of anisotropies in the cosmic microwave background, rules to construct a quantized universe is proposed based on the dynamical triangulation method of the simplicial quantum gravity. A $d$-dimensional universe having the topology $D^d$ is created numerically in terms of a simplicial manifold with $d$-simplices as the building blocks. The space coordinates of a universe are identified on the boundary surface $S^{d-1}$, and the time coordinate is defined along the direction perpendicular to $S^{d-1}$. Numerical simulations are made mainly for 2-dimensional universes, and analyzed to examine appropriateness of the construction rules by comparing to analytic results of the matrix model and the Liouville theory. Furthermore, a simulation in 4-dimension is made, and the result suggests an ability to analyze the observations on anisotropies by comparing to the scalar curvature correlation of a $S^2$-surface formed as the last scattering surface in the $S^3$ universe.Comment: 27pages,18figures,using jpsj.st

Supersymmetric Wilson Loops in IIB Matrix Model

We show that the supersymmetric Wilson loops in IIB matrix model give a transition operator from reduced supersymmetric Yang-Mills theory to supersymmetric space-time theory. In comparison with Green-Schwarz superstring we identify the supersymmetric Wilson loops with the asymptotic states of IIB superstring. It is pointed out that the supersymmetry transformation law of the Wilson loops is the inverse of that for the vertex operators of massless modes in the U(N) open superstring with Dirichlet boundary condition.Comment: 10 pages, Latex, minor typos correcte

Lattice Distortion and Magnetism of 3d-t2gt_{2g} Perovskite Oxides

Several puzzling aspects of interplay of the experimental lattice distortion and the the magnetic properties of four narrow $t_{2g}$-band perovskite oxides (YTiO$_3$, LaTiO$_3$, YVO$_3$, and LaVO$_3$) are clarified using results of first-principles electronic structure calculations. First, we derive parameters of the effective Hubbard-type Hamiltonian for the isolated $t_{2g}$ bands using newly developed downfolding method for the kinetic-energy part and a hybrid approach, based on the combination of the random-phase approximation and the constraint local-density approximation, for the screened Coulomb interaction part. Then, we solve the obtained Hamiltonian using a number of techniques, including the mean-field Hartree-Fock (HF) approximation, the second-order perturbation theory for the correlation energy, and a variational superexchange theory. Even though the crystal-field splitting is not particularly large to quench the orbital degrees of freedom, the crystal distortion imposes a severe constraint on the form of the possible orbital states, which favor the formation of the experimentally observed magnetic structures in YTiO$_3$, YVO_, and LaVO$_3$ even at the HF level. Beyond the HF approximation, the correlations effects systematically improve the agreement with the experimental data. Using the same type of approximations we could not reproduce the correct magnetic ground state of LaTiO$_3$. However, we expect that the situation may change by systematically improving the level of approximations for dealing with the correlation effects.Comment: 30 pages, 17 figures, 8 tables, high-quality figures are available via e-mai