Regge gravity on general triangulations

We investigate quantum gravity in four dimensions using the Regge approach on triangulations of the four-torus with general, non-regular incidence matrices. We find that the simplicial lattice tends to develop spikes for vertices with low coordination numbers even for vanishing gravitational coupling. Different to the regular, hypercubic lattices almost exclusively used in previous studies, we find now that the observables depend on the measure. Computations with nonvanishing gravitational coupling still reveal the existence of a region with well-defined expectation values. However, the phase structure depends on the triangulation. Even with additional higher- order terms in the action the critical behavior of the system changes with varying (local) coordination numbers.Comment: uuencoded postscript file, 16 page

SU(2) potentials in quantum gravity

We present investigations of the potential between static charges from a simulation of quantum gravity coupled to an SU(2) gauge field on $6^{3}\times 4$ and $8^{3}\times 4$ simplicial lattices. In the well-defined phase of the gravity sector where geometrical expectation values are stable, we study the correlations of Polyakov loops and extract the corresponding potentials between a source and sink separated by a distance $R$. In the confined phase, the potential has a linear form while in the deconfined phase, a screened Coulombic behavior is found. Our results indicate that quantum gravitational effects do not destroy confinement due to non-abelian gauge fields.Comment: 3 pages, contribution to Lattice 94 conference, uuencoded compressed postscript fil

Static Quark Potentials in Quantum Gravity

We present potentials between static charges from simulations of quantum gravity coupled to an SU(2) gauge field on $6^{3}\times 4$ and $8^{3}\times 4$ simplicial lattices. The action consists of the gravitational term given by Regge's discrete version of the Euclidean Einstein action and a gauge term given by the Wilson action, with coupling constants $m_{p}^{2}$ and $\beta$ respectively. In the well-defined phase of the gravity sector where geometrical expectation values are stable, we study the correlations of Polyakov loops and extract the corresponding potentials between a source and sink separated by a distance $R$. We compare potentials on a flat simplicial lattice with those on a fluctuating Regge skeleton. In the confined phase, the potential has a linear form while in the deconfined phase, a screened Coulombic behavior is found. Our results indicate that quantum gravitational effects do not destroy confinement due to non-abelian gauge fields.Comment: 8 pages, to be published in Phys. Lett. B, uuencoded compressed postscript file

Indications for Criticality at Zero Curvature in a 4d Regge Model of Euclidean Quantum Gravity

We re-examine the approach to four-dimensional Euclidean quantum gravity based on the Regge calculus. A cut-off on the link lengths is introduced and consequently the gravitational coupling and the cosmological constant become independent parameters. We determine the zero curvature, $=0$, line in the coupling constant plane by numerical simulations. When crossing this line we find a strong, probably first order, phase transition line with indications of a second order endpoint. Beyond the endpoint the transition through the $=0$ line appears to be a crossover. Previous investigations, using the Regge or the Dynamical Triangulation approach, dealt with a limit in which the first order transition prevails.Comment: Contribution to the lattice 2003 Tsukuba symposiu

Spins coupled to a Z2Z_2-Regge lattice in 4d

We study an Ising spin system coupled to a fluctuating four-dimensional $Z_2$-Regge lattice and compare with the results of the four-dimensional Ising model on a regular lattice. Particular emphasis is placed on the phase transition of the spin system and the associated critical exponents. We present results from finite-size scaling analyses of extensive Monte Carlo simulations which are consistent with mean-field predictions.Comment: Lattice2001(surfaces), 3 pages, 2 figure