arXiv subjects

H. S. Egawa

Publications and source records attributed to H. S. Egawa.

15 recordsLinked to original sources

arXiv2003

Fractal Structure of 4D Euclidean Simplicial Manifold

The fractal properties of four-dimensional Euclidean simplicial manifold generated by the dynamical triangulation are analyzed on the geodesic distance D between two vertices instead of the usual scale between two simplices. In order to make more unambiguous measurement of the fractal dimension, we employ a different approach from usual, by measuring the box-counting dimension which is computed by counting the number of spheres with the radius D within the manifold. The numerical result is consistent to the result of the random walk model in the branched polymer region. We also measure the box-counting dimension of the manifold with additional matter fields. Numerical results suggest that the fractal dimension takes value of slightly more than 4 near the critical point. Furthermore, we analyze the correlation functions as functions of the geodesic distance. Numerically, it is suggested that the fractal structure of four-dimensional simplicial manifold can be properly analyzed in terms of the distance between two vertices. Moreover, we show that the behavior of the correlation length regards the phase structure of 4D simplicial manifold.

hep-lat↗

arXiv2002

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.

hep-lat↗

arXiv2001

Clear Evidence of a Continuum Theory of 4D Euclidean Simplicial Quantum Gravity

Four-dimensional (4D) simplicial quantum gravity coupled to both scalar fields (N_X) and gauge fields (N_A) has been studied using Monte-Carlo simulations. The matter dependence of the string susceptibility exponent gamma^{(4)} is estimated. Furthermore, we compare our numerical results with Background-Metric-Independent (BMI) formulation conjectured to describe the quantum field theory of gravity in 4D. The numerical results suggest that the 4D simplicial quantum gravity is related to the conformal gravity in 4D. Therefore, we propose a phase structure in detail with adding both scalar and gauge fields and discuss the possibility and the property of a continuum theory of 4D Euclidean simplicial quantum gravity.

hep-lat↗

arXiv2000

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.

hep-th↗

arXiv2000

Numerical Analysis of the Double Scaling Limit in the bosonic part of the IIB Matrix Model

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.

hep-lat↗

arXiv2000

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.

hep-lat↗

arXiv2000

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.

hep-lat↗

arXiv1999

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 ($χ$) 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.

hep-lat↗

arXiv1998

Further Evidence of a Smooth Phase in 4D Simplicial Quantum Gravity

Four-dimensional (4D) simplicial quantum gravity coupled to U(1) gauge fields has been studied using Monte-Carlo simulations. A negative string susceptibility exponent is observed beyond the phase-transition point, even if the number of vector fields (NV) is 1. We find a scaling relation of the boundary volume distributions in this new phase. This scaling relation suggests a fractal structure similar to that of 2D quantum gravity. Furthermore, evidence of a branched polymer-like structure is suggested far into the weak-coupling region, even for NV > 1. As a result, we propose new phase structures and discuss the possibility of taking the continuum limit in a certain region between the crumpled and branched polymer phases.

hep-lat↗

arXiv1998

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.

hep-lat↗

arXiv1998

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.

hep-lat↗

arXiv1997

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.

hep-lat↗

arXiv1997

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 ($\tildeγ_{st}$) 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 $\tildeγ_{st} \approx -0.5$. 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 $γ_{st}^{(3)} \approx γ_{st}^{(4)} \approx 0$. The existence of common structures in simplicial quantum gravity is also discussed.

hep-lat↗

arXiv1996

Scaling Behavior in 4D Simplicial Quantum Gravity

Scaling relations in four-dimensional simplicial quantum gravity are proposed using the concept of the geodesic distance. Based on the analogy of a loop length distribution in the two-dimensional case, the scaling relations of the boundary volume distribution in four dimensions are discussed in three regions: the strong-coupling phase, the critical point and the weak-coupling phase. In each phase a different scaling behavior is found.

hep-lat↗

arXiv1996

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.

hep-lat↗