Topology of Boundary Surfaces in 3D Simplicial Gravity

A model of simplicial quantum gravity in three dimensions(3D) was investigated numerically based on the technique of dynamical triangulation (DT). We are concerned with the genus of surfaces appearing on boundaries (i.e., sections) of a 3D DT manifold with $S^{3}$ topology. Evidence of a scaling behavior of the genus distributions of boundary surfaces has been found.Comment: 3 pages, latex, 4 ps figures, uses espcrc2.sty. Talk presented at LATTICE'97(gravity

Geometry of 4d Simplicial Quantum Gravity with a U(1) Gauge Field

The geometry of 4D simplicial quantum gravity with a U(1) gauge field is studied numerically. The phase diagram shows a continuous transition when gravity is coupled with a U(1) gauge field. At the critical point measurements of the curvature distribution of S^4 space shows an inflated geometry with homogeneous and symmetric nature. Also, by choosing a 4-simplex and fixing the scalar curvature geometry of the space is measured.Comment: 3 pages, 2 eps figure. Talked at Lattice 2000 (Gravity

Grand-Canonical simulation of 4D simplicial quantum gravity

A thorough numerical examination for the field theory of 4D quantum gravity (QG) with a special emphasis on the conformal mode dependence has been studied. More clearly than before, we obtain the string susceptibility exponent of the partition function by using the Grand-Canonical Monte-Carlo method. Taking thorough care of the update method, the simulation is made for 4D Euclidean simplicial manifold coupled to $N_X$ scalar fields and $N_A$ U(1) gauge fields. The numerical results suggest that 4D simplicial quantum gravity (SQG) can be reached to the continuum theory of 4D QG. We discuss the significant property of 4D SQG.Comment: 3 pages, 2 figures, LaTeX, Lattice2002(Gravity

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 ($N_{V}=1$) is smooth as compared with the pure gravity($N_{V}=0$). The node susceptibility ($\chi$) is studied in the finite size scaling method. At the critical point, the node distribution has a sharp peak in contrast to the double peak in the pure gravity. From the numerical results, we expect that 4D simplicial quantum gravity with U(1) vector fields has higher order phase transition than 1st order, which means the possibility to take the continuum limit at the critical point.Comment: 3 pages, latex, 3 eps figures, uses espcrc2.sty. Talk presented at LATTICE99(gravity

Random Surfaces in Three-Dimensional Simplicial Gravity

A model of simplicial quantum gravity in three dimensions is investigated numerically based on the technique of the dynamical triangulation (DT). We are concerned with the surfaces appearing on boundaries (i.e., sections) of three-dimensional DT manifold with $S^{3}$ topology. A new scaling behavior of genus distributions of boundary surfaces is found.Furthermore, these surfaces are compared with the random surfaces generated by the two-dimensional DT method which are well known as a correct discretized method of the two-dimensional quantum gravity.Comment: 12 pages, Latex, 7 Postscript figures, uses psfig.sty and cite.st

Common Structures in 2,3 and 4D Simplicial Quantum Gravity

Two kinds of statistical properties of dynamical-triangulated manifolds (DT mfds) have been investigated. First, the surfaces appearing on the boundaries of 3D DT mfds were investigated. The string-susceptibility exponent of the boundary surfaces ($\tilde{\gamma}_{st}$) of 3D DT mfds with $S^{3}$ topology near to the critical point was obtained by means of a MINBU (minimum neck baby universes) analysis; actually, we obtained $\tilde{\gamma}_{st} \approx -0.5$. Second, 3 and 4D DT mfds were also investigated by determining the string-susceptibility exponent near to the critical point from measuring the MINBU distributions. As a result, we found a similar behavior of the MINBU distributions in 3 and 4D DT mfds, and obtained $\gamma_{st}^{(3)} \approx \gamma_{st}^{(4)} \approx 0$. The existence of common structures in simplicial quantum gravity is also discussed.Comment: 3 pages, latex, 3 ps figures, uses espcrc2.sty. Talk presented at LATTICE97(gravity

Common Structures in Simplicial Quantum Gravity

The statistical properties of dynamically triangulated manifolds (DT mfds) in terms of the geodesic distance have been studied numerically. The string susceptibility exponents for the boundary surfaces in three-dimensional DT mfds were measured numerically. For spherical boundary surfaces, we obtained a result consistent with the case of a two-dimensional spherical DT surface described by the matrix model. This gives a correct method to reconstruct two-dimensional random surfaces from three-dimensional DT mfds. Furthermore, a scaling property of the volume distribution of minimum neck baby universes was investigated numerically in the case of three and four dimensions, and we obtain a common scaling structure near to the critical points belonging to the strong coupling phase in both dimensions. We have evidence for the existence of a common fractal structure in three- and four-dimensional simplicial quantum gravity.Comment: 10 pages, latex, 6 ps figures, uses cite.sty and psfig.st

Numerical Analysis of the Double Scaling Limit in the IIB 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.Comment: 9pages, latex, 4 figures, uses psfig.sty, corrected some typos and reference

Scaling Structures in Four-dimensional Simplicial Gravity

Four-dimensional(4D) spacetime structures are investigated using the concept of the geodesic distance in the simplicial quantum gravity. On the analogy of the loop length distribution in 2D case, the scaling relations of the boundary volume distribution in 4D are discussed in various coupling regions i.e. strong-coupling phase, critical point and weak-coupling phase. In each phase the different scaling relations are found.Comment: 4 pages, latex, 4 ps figures, uses espcrc2.sty. Talk presented at LATTICE96(gravity). All figures and its captions have been improve