Phases and fractal structures of three-dimensional simplicial gravity

We study phases and fractal structures of three-dimensional simplicial quantum gravity by the Monte-Carlo method. After measuring the surface area distribution (SAD) which is the three-dimensional analog of the loop length distribution (LLD) in two-dimensional quantum gravity, we classify the fractal structures into three types: (i) in the hot (strong coupling) phase, strong gravity makes the space-time one crumpled mother universe with small fluctuating branches around it. This is a crumpled phase with a large Hausdorff dimension d_{\mbox{\tiny H}} \simeq 5. The topologies of cross-sections are extremely complicated. (ii) at the critical point, we observe that the space-time is a fractal-like manifold which has one mother universe with small and middle size branches around it. The Hausdorff dimension is d_{\mbox{\tiny H}} \simeq 4. We observe some scaling behaviors for the cross-sections of the manifold. This manifold resembles the fractal surface observed in two-dimensional quantum gravity. (iii) in the cold (weak coupling) phase, the mother universe disappears completely and the space-time seems to be the branched-polymer with a small Hausdorff dimension d_{\mbox{\tiny H}} \simeq 2. Almost all of the cross-sections have the spherical topology $S^2$ in the cold phase.Comment: 14 pages, latex file, 5 Postscript figures, use psfig.st

Birth and Growth of Two-dimensional Universe

A master equation for the evolution of two-dimensional universe is derived based on the simplicial quantum gravity regarding the evolution as the Markov process of a space-time lattice. Three typical phases, expanding, elongating and collapsing phase, which have been found in the numerical simulation, are studied together with their boundaries, analytically. Asymptotic solutions of the evolution equation for statistical quantities, such as averaged area, boundary length, and correlation of fluctuations, are obtained for each phase and boundary.After introducing a physical time the cosmological significance of each phase is discussed

Complex Structures Defined on Dynamically Triangulated Surfaces

A method to define the complex structure and separate the conformal mode is proposed for a surface constructed by two-dimensional dynamical triangulation. Applications are made for surfaces coupled to matter fields such as $n$ scalar fields ($n=0,1$ and $4$) and $m$ Ising spins ($m=1$ and $3$). We observe a well-defined complex structure for cases when the matter central charges are less than and equal to one, while it becomes unstable beyond $c=1$. This can be regarded as the transition expected in analytic theories.Comment: 8 pages, 5 Postscript figure

Type IIB Random Superstrings

We consider random superstrings of type IIB in $d$-dimensional space. The discretized action is constructed from the supersymetric matrix model, which has been proposed as a constructive definition of superstring theory. Our action is invariant under the local N=2 super transformations, and doesn't have any redundant fermionic degrees of freedom.Comment: 6 pages, Latex, 3 postscript figures, some expressions and format are improve

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

Analyzing WMAP Observation by Quantum Gravity

The angular power spectra of cosmic microwave background are analyzed under the light of the evolutional scenario of the universe based on the renormalizable quantum theory of gravity in four dimensions. The equation of evolution is solved numerically fixing the power law spectrum predicted by the conformal gravity for the initial condition. The equation requires to introduce a dynamical energy scale about 10^{17}GeV, where the inflationary space-time evolution makes a transition to the big-bang of the conventional Friedmann universe. The quality of fit to the three-year data of WMAP implies the possibility to understand the observation by quantum gravity.Comment: 12 pages, 7 figure

CMB Anisotropies Reveal Quantized Gravity

A novel primordial spectrum with a dynamical scale of quantum gravity origin is proposed to explain the sharp fall off of the angular power spectra at low multipoles in the COBE and WMAP observations. The spectrum is derived from quantum fluctuations of the scalar curvature in a renormalizable model of induced gravity. This model describes the very early universe by the conformal field fluctuating about an inflationary background with the expansion time constant of order of the Planck mass.Comment: 12 pages, 2 figure

量子カオスについて(基研短期研究会「数理物理学における非線形問題」,研究会報告)

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