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

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.Comment: 12 pages, latex, 10 postscript figures, uses psfig.sty and cite.st

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.Comment: 18 pages, latex, 6 figures, uses psfig.st