Common structures in simplicial quantum gravity

Abstract

Statistical properties of dynamically triangulated manifolds (DT mfds) in terms of the geodesic distance are studied numerically. The string susceptibility exponents for the boundary surfaces in three-dimensional DT mfds are measured numerically. For spherical boundary surfaces, we obtain a result consistent with the case of a two-dimensional spherical DT surface described by the matrix model. This gives a correct method to reconstruct two-dimensional random surfaces from three-dimensional DT mfds. Furthermore, a scaling property of the volume distribution of minimum neck baby universes is investigated numerically in the case of three and four dimensions, and we obtain a common scaling structure near to the critical points belonging to the strong coupling phase in both dimensions. We have evidence for the existence of a common fractal structure in three- and four-dimensional simplicial quantum gravity.