Shinichi Horata

Conformal Algebra and Physical States in a Non-Critical 3-Brane on R ×S3

A world-volume model of a non-critical 3-brane is quantized in a strong coupling phase in which fluctuations of the conformal mode become dominant. This phase, called the conformal-mode dominant phase, is realized at very high energies far beyond the Planck mass scale. We separately treat the conformal mode and the traceless mode and quantize the conformal mode non-perturbatively, while the traceless mode is treated in a perturbative method that is renormalizable and asymptotically free. In the conformal-mode dominant phase, the coupling of the traceless mode vanishes, and the world-volume dynamics are described by a four-dimensional conformal field theory (CFT4). We canonically quantize this model on R × S 3 , where the dynamical fields are expanded in spherical tensor harmonics on S 3 , which include both positive-metric and negative-metric modes. Conformal charges and a conformal algebra are constructed. They yield strong constraints on physical states. We find that all negative-metric modes are related to positive-metric modes through the charges, and thus negative-metric modes are themselves not independent physical modes. Physical states satisfying the conformal invariance conditions are given by particular combinations of positive-metric and negative-metric modes. An infinite number of such physical states are constructed. In the Appendices, we construct spherical vector and tensor harmonics on S 3 in practical forms using the Wigner D functions and the Clebsch-Gordan coefficients and calculate the integrals of three and four products of these harmonics over S 3 .

Phase Structure of Four-Dimensional Simplicial Quantum Gravity with a U(1) Gauge Field

The phase structure of four-dimensional simplicial quantum gravity coupled to U(1) gauge fields has been studied using Monte-Carlo simulations. The smooth phase is found in the intermediate region between the crumpled phase and the branched polymer phase. This new phase has a negative string susceptibility exponent, even if the number of vector fields (Nv) is 1. The phase transition between the crumpled phase and the smooth phase has been studied by a finite size scaling method. From the numerical results, we expect that this model (coupled to one gauge field) has a higher order phase transition than first order, which means the possibility to take the continuum limit at the critical point. Furthermore, we consider a modification of the balls-in-boxes model for a clear understanding of the relation between the numerical results and the analytical one.The phase structure of four-dimensional simplicial quantum gravity coupled to a U(1) gauge field is investigated numerically with the dynamical triangulation method. A smooth phase is found in the region between the crumpled phase and the branched polymer phase. This new phase has a negative string susceptibility exponent. The phase transition between the smooth phase and the crumpled phase is studied using the finite size scaling method. From the numerical results we conclude that this model has a phase transition that is higher than first-order. Numerical results suggest a possibility of the existence of the continuum limit at the critical point.

Space-time evolution and CMB anisotropies from quantum gravity

We propose an evolutional scenario of the universe which starts from quantum states with conformal invariance, passing through the inflationary era, and then makes a transition to the conventional Einstein space-time. The space-time dynamics is derived from the renormalizable higher-derivative quantum gravity on the basis of a conformal gravity in four dimensions. Based on the linear perturbation theory in the inflationary background, we simulate evolutions of gravitational scalar, vector, and tensor modes, and evaluate the spectra at the transition point located at the beginning of the big bang. The obtained spectra cover the range of the primordial spectra for explaining the anisotropies in the homogeneous cosmic microwave background.

Matter Dependence of the String Susceptibility Exponent in Four-Dimensional Simplicial Quantum Gravity

The dependence of the number of vector and scalar fields on the string susceptibility exponent is evaluated numerically for four-dimensional simplicial quantum gravity using the grand canonical ensemble method. The numerical result indicates that the four-dimensional simplicial quantum gravity reproduces well predictions of the four-dimensional conformal gravity.

Numerical analysis of the double scaling limit in the bosonic part of the II-B matrix model☆

The bosonic IIB matrix model is studied using a numerical method. This model contains the bosonic part of the IIB matrix model conjectured to be a non-perturbative definition of the type IIB superstring theory. The large N scaling behavior of the model is shown performing a Monte Carlo simulation. The expectation value of the Wilson loop operator is measured and the string tension is estimated. The numerical results show the prescription of the double scaling limit.Abstract The bosonic IIB matrix model, which contains the bosonic part of the IIB matrix model conjectured to be a non-perturbative definition of the type IIB superstring theory, is studied using a numerical method. The large N scaling behavior of the model is shown performing a Monte Carlo simulation. The expectation value of the Wilson loop operator is measured and the string tension is estimated. From the numerical results, the prescription of the double scaling limit is obtained.

Phase transition of 4D simplicial quantum gravity with U (1) gauge field

The phase transition of 4D simplicial quantum gravity coupled to U(1) gauge fields is studied using Monte-Carlo simulations. The phase transition of the dynamical triangulation model with vector field (

Analyzing WMAP Observation by Quantum Gravity

N_{V}=1

Grand-canonical simulation of 4D simplicial quantum gravity

) is smooth as compared with the pure gravity(

Clear evidence of a continuum theory of 4D Euclidean simplicial quantum gravity

N_{V}=0

Fractal structure of 4D euclidean simplicial manifold

). The node susceptibility (