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

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

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

Renormalizable 4D Quantum Gravity as A Perturbed Theory from CFT

We study the renormalizable quantum gravity formulated as a perturbed theory from conformal field theory (CFT) on the basis of conformal gravity in four dimensions. The conformal mode in the metric field is managed non-perturbatively without introducing its own coupling constant so that conformal symmetry becomes exact quantum mechanically as a part of diffeomorphism invariance. The traceless tensor mode is handled in the perturbation with a dimensionless coupling constant indicating asymptotic freedom, which measures a degree of deviation from CFT. There are no massive ghosts because they are not gauge invariant in this formulation. Higher order renormalization is carried out using dimensional regularization, in which the Wess-Zumino integrability condition is applied to reduce indefiniteness existing in higher-derivative actions. The effective action of quantum gravity improved by renormalization group is obtained. We then make clear that conformal anomalies are indispensable quantities to preserve diffeomorphism invariance. Anomalous scaling dimensions of the cosmological constant and the Planck mass are calculated. The effective cosmological constant is obtained in the large number limit of matter fields.Comment: 51 pages, 12 figure

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

Strong correlation effects of the Re 5dd electrons on the metal-insulator transition in Ca2_2FeReO6_6

We have investigated the electronic structure of polycrystalline Ca$_2$FeReO$_6$ using photoemission spectroscopy and band-structure calculations within the local-density approximation+$U$ (LDA+$U$) scheme. In valence-band photoemission spectra, a double-peak structure which is characteristic of the metallic double perovskite series has been observed near the Fermi level ($E_{\rm F}$), although it is less distinct compared to the Sr$_2$FeMoO$_6$ case. The leading near-$E_{\rm F}$ structure has a very weak spectral weight at $E_{\rm F}$ above the metal-insulator transition (MIT) temperature $T_{\rm MI}$ of $\sim$140 K, and it loses the $E_{\rm F}$ weight below $T_{\rm MI}$, forming a small energy gap. To reproduce this small energy gap in the calculation, we require a very large effective $U$ ($U_{\rm eff}$) for Re (4 eV) in addition to a relatively large $U_{\rm eff}$ for Fe (4 eV). Although the most of the experimental features can be interpreted with the help of the band theory, the overall agreement between the theory and the experiment was not satisfactory. We demonstrate that the effective transfer integral between Fe and Re is actually smaller than that between Fe and Mo in Ca$_2$FeMoO$_6$, which can explain both MIT and very high ferrimagnetic transition temperature.Comment: 7 pages text, 5 figures, to be pulished in Phys. Rev.

Finite element based fatigue life prediction of cylinder head for two-stroke linear engine using stress-life approach

Abstract: This describes the finite element based fatigue life prediction of cylinder head for two-stroke linear engine subjected to variable amplitude loading applicable to electric power generation. A set of Al-alloys, cast iron and forged steel for cylinder head are considered in this study