Wolfgang Beirl

Influence of the measure on simplicial quantum gravity in four dimensions.

We investigate the influence of the measure in path integral for Euclidean quantum gravity in four dimensions within the Regge calculus. The action is bounded without additional terms by fixing the average lattice spacing. We set the length scale by a parameter β and consider a scale-invariant and a uniform measure. In the low-β region we observe a phase with negative curvature and a homogeneous distribution of the link lengths independent of the measure. The large-β region is characterized by inhomogeneous link length distributions with spikes and positive curvature depending on the measure

The Well defined phase of simplicial quantum gravity in four-dimensions

We analyze simplicial quantum gravity in four dimensions using the Regge approach. The existence of an entropy dominated phase with small negative curvature is investigated in detail. It turns out that observables of the system possess finite expectation values although the Einstein-Hilbert action is unbounded. This well-defined phase is found to be stable for a one-parameter family of measures. A preliminary study indicates that the influence of the lattice size on the average curvature is small. We compare our results with those obtained by dynamical triangulation and find qualitative correspondence.

Correlation functions in lattice formulations of quantum gravity

Abstract We compare different models of a quantum theory of four-dimensional lattice gravity based on Regges original proposal. From Monte Carlo simulations we calculate two-point functions between geometrical quantities and estimate the masses of the corresponding interaction particles.

Phase structure and graviton propagators in lattice formulations of four-dimensional quantum gravity

We examine the phase structure of standard Regge calculus in four dimensions and compare our Monte Carlo results with those of the -Regge model as well as with another formulation of lattice gravity derived from group-theoretical considerations. Within all of the three models of quantum gravity we find an extension of the well-defined phase to negative gravitational couplings and a new phase transition. In contrast to the well known transition at positive coupling there is evidence for a continuous phase transition which is essential for a continuum limit. We calculate two-point functions between geometrical quantities at the corresponding critical point and estimate the masses of the respective interaction particles.

Is there quantum gravity in two dimensions

Abstract A hybrid model that allows one to interpolate between the (original) Regge approach and dynamical triangulation is introduced. The gained flexibility in the measure is exploited to study dynamical triangulation in a fixed geometry. Our numerical results support KPZ exponents. A critical assessment concerning the apparent lack of gravitational effects in two dimensions follows.

Gravitational action versus entropy on simplicial lattices in four dimensions

Abstract We investigate quantum gravity on simplicial lattices using Regge calculus with special emphasize on the problem of the unbounded action. The role of the entropy for the path integral is discussed in detail. Our numerical results show further evidence for the existence of an entropy dominated region with well defined expectation values even for unbounded action. Analyses are performed both for the standard regular triangulation of the 4-torus and for irregularly triangulated lattices obtained by insertion of vertices using barycentric subdivision.

The phase structure of pure Regge gravity

We examine the phase structure of pure Regge gravity in four dimensions and compare our Monte Carlo results with Z 2 -link Regge-theory as well as with another formulation of lattice gravity derived from group theoretical considerations. Within all three models we find an extension of the well-defined phase to negative gravitational coupling and a new phase transition. In contrast to the well-known transition at positive coupling there is evidence for a continuous phase transition which might be essential for a possible continuum limit.

Phase diagram of Regge quantum gravity coupled to SU(2) gauge theory

We analyze Regge quantum gravity coupled to SU(2) gauge theory on 4{sup 3}{times}2, 6{sup 3}{times}4, and 8{sup 3}{times}4 simplicial Euclidean lattices. It turns out that the window of the well-defined phase of the gravity sector where geometrical expectation values are stable extends to negative gravitational couplings as well as to gauge couplings across the deconfinement phase transition. We study the string tension from Polyakov loops, compare with the {beta} function of pure gauge theory, and conclude that a physical limit through scaling is possible. {copyright} {ital 1996 The American Physical Society.}

Static quark potentials in quantum gravity

Abstract We present potentials between static charges from simulations of quantum gravity coupled to an SU(2) gauge field on 6 3 × 4 and 8 3 × 4 simplicial lattices. The action consists of the gravitational term given by Regges discrete version of the Euclidean Einstein action and a gauge term given by the Wilson action, with coupling constants m p 2 and β 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.

Two-point functions of four-dimensional simplicial quantum gravity

Abstract We investigate the interaction mechanism of pure quantum gravity in Regge discretization. We compute volume-volume and link-link correlation functions. In a preliminary analysis the forces turn out to be of Yukawa type, at least on our finite lattice being away from the continuum limit.