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

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

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

Electronic states of metallic and semiconducting carbon nanotubes with bond and site disorder

Disorder effects on the density of states in carbon nanotubes are analyzed by a tight binding model with Gaussian bond or site disorder. Metallic armchair and semiconducting zigzag nanotubes are investigated. In the strong disorder limit, the conduction and valence band states merge, and a finite density of states appears at the Fermi energy in both of metallic and semiconducting carbon nanotubes. The bond disorder gives rise to a huge density of states at the Fermi energy differently from that of the site disorder case. Consequences for experiments are discussed.Comment: Phys. Rev. B: Brief Reports (to be published). Related preprints can be found at http://www.etl.go.jp/~harigaya/NEW.htm

Non-linear Structures in Non-critical NSR String

We investigate the Ward identities of the \W_{\infty} symmetry in the super-Liouville theory coupled to the super-conformal matter of central charge ${\hat c}_M = 1-2(p-q)^2 /pq$. The theory is classified into two chiralities. For the positive chirality, all gravitationally dressed scaling operators are generated from the $q-1$ gravitational primaries by acting one of the ring generators in the R-sector on them repeatedly. After fixing the normalizations of the dressed scaling operators, we find that the Ward identities are expressed in the form of the {\it usual} \W_q algebra constraints as in the bosonic case: \W^{(k+1)}_n \tau =0, $(k=1,\cdots,q-1 ;~ n \in {\bf Z}_{\geq 1-k})$, where the equations for even and odd $n$ come from the currents in the NS- and the R-sector respectively. The non-linear terms come from the anomalous contributions at the boundaries of moduli space. The negative chirality is defined by interchanging the roles of $p$ and $q$. Then we get the \W_p algebra constraints.Comment: 22 pages, Latex file, YITP/U-94-16, UT-Komaba/94-1

Dimerization structures on the metallic and semiconducting fullerene tubules with half-filled electrons

Possible dimerization patterns and electronic structures in fullerene tubules as the one-dimensional pi-conjugated systems are studied with the extended Su-Schrieffer-Heeger model. We assume various lattice geometries, including helical and nonhelical tubules. The model is solved for the half-filling case of $\pi$-electrons. (1) When the undimerized systems do not have a gap, the Kekule structures prone to occur. The energy gap is of the order of the room temperatures at most and metallic properties would be expected. (2) If the undimerized systems have a large gap (about 1eV), the most stable structures are the chain-like distortions where the direction of the arranged trans-polyacetylene chains is along almost the tubular axis. The electronic structures are ofsemiconductors due to the large gap.Comment: submitted to Phys. Rev. B, pages 15, figures 1

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

Teleportation and entanglement distillation in the presence of correlation among bipartite mixed states

The teleportation channel associated with an arbitrary bipartite state denotes the map that represents the change suffered by a teleported state when the bipartite state is used instead of the ideal maximally entangled state for teleportation. This work presents and proves an explicit expression of the teleportation channel for the teleportation using Weyl's projective unitary representation of the space of 2n-tuples of numbers from Z/dZ for integers d>1, n>0, which has been known for n=1. This formula allows any correlation among the n bipartite mixed states, and an application shows the existence of reliable schemes for distillation of entanglement from a sequence of mixed states with correlation.Comment: 12 pages, 1 figur

RNA secondary structure prediction from multi-aligned sequences

It has been well accepted that the RNA secondary structures of most functional non-coding RNAs (ncRNAs) are closely related to their functions and are conserved during evolution. Hence, prediction of conserved secondary structures from evolutionarily related sequences is one important task in RNA bioinformatics; the methods are useful not only to further functional analyses of ncRNAs but also to improve the accuracy of secondary structure predictions and to find novel functional RNAs from the genome. In this review, I focus on common secondary structure prediction from a given aligned RNA sequence, in which one secondary structure whose length is equal to that of the input alignment is predicted. I systematically review and classify existing tools and algorithms for the problem, by utilizing the information employed in the tools and by adopting a unified viewpoint based on maximum expected gain (MEG) estimators. I believe that this classification will allow a deeper understanding of each tool and provide users with useful information for selecting tools for common secondary structure predictions.Comment: A preprint of an invited review manuscript that will be published in a chapter of the book `Methods in Molecular Biology'. Note that this version of the manuscript may differ from the published versio