Grand-canonical simulation of two-dimensional simplicial gravity

The string susceptibility exponents of dynamically triangulated 2-dimensional surfaces with various topologies, such as a sphere, torus and double-torus, were calculated by the grand-canonical Monte Carlo method. These simulations were made for surfaces coupled to $d$-Ising spins ($d$=0,1,2,3,5). In each simulation the area of surface was constrained to within 1000 to 3000 of triangles, while maintaining the detailed-balance condition. The numerical results show excellent agreement with theoretical predictions as long as $d \leq 2$.Comment: 9 pages, Latex include 5 postscript figures, using psfig.sty and cite.st

Minbu distribution of two dimensional quantum gravity: simulation result and semiclassical analysis

We analyse MINBU distribution of 2 dimensional quantum gravity. New data of R^2-gravity by the Monte Carlo simulation and its theoretical analysis by the semiclassical approach are presented. The cross-over phenomenon takes place at some size of the baby universe where the randomness competes with the smoothing force of R^2-term. The dependence on the central charge c_m\ and on the R^2-coupling are explained for the ordinary 2d quantum gravity and for R^2-gravity. The R^2-Liouville solution plays the central role in the semiclassical analysis. A total derivative term (surface term) and the infrared regularization play important roles . The surface topology is that of a sphere

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

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

Introducing Dynamical Triangulations to the Type IIB Superstrings

In order to consider non-perturbative effects of superstrings, we try to apply dynamical triangulations to the type IIB superstrings. The discretized action is constructed from the type IIB matrix model proposed as a constructive definition of superstring theory. The action has the local N=2 supersymmetry explicitly, and has no extra fermionic degrees of freedom. We evaluate the partition function for some simple configurations and discuss constraints required from the finiteness of partition functions.Comment: LATTICE99, 3 pages, LaTeX with 2 figures, espcrc2.st

Hadron-hadron interaction from SU(2) lattice QCD

We evaluate interhadron interactions in two-color lattice QCD from Bethe-Salpeter amplitudes on the Euclidean lattice. The simulations are performed in quenched SU(2) QCD with the plaquette gauge action at $\beta = 2.45$ and the Wilson quark action. We concentrate on S-wave scattering states of two scalar diquarks. Evaluating different flavor combinations with various quark masses, we try to find out the ingredients in hadronic interactions. Between two scalar diquarks ($u C\gamma_5 d$, the lightest baryon in SU(2) system), we observe repulsion in short-range region, even though present quark masses are not very light. We define and evaluate the "quark-exchange part" in the interaction, which is induced by adding quark-exchange diagrams, or equivalently, by introducing Pauli blocking among some of quarks. The repulsive force in short-distance region arises only from the "quark-exchange part", and disappears when quark-exchange diagrams are omitted. We find that the strength of repulsion grows in light quark-mass regime and its quark-mass dependence is similar to or slightly stronger than that of the color-magnetic interaction by one-gluon-exchange (OGE) processes. It is qualitatively consistent with the constituent-quark model picture that a color-magnetic interaction among quarks is the origin of repulsion. We also find a universal long-range attractive force, which enters in any flavor channels of two scalar diquarks and whose interaction range and strength are quark-mass independent. The weak quark-mass dependence of interaction ranges in each component implies that meson-exchange contributions are small and subdominant, and the other contributions, {\it ex.} flavor exchange processes, color-Coulomb or color-magnetic interactions, are considered to be predominant, in the quark-mass range we evaluated.Comment: 14 pages, 20 figure