CURVATURE AND SCALING IN 4D DYNAMICAL TRIANGULATION

We study the average number of simplices N'(r) at geodesic distance r in the dynamical triangulation model of euclidean quantum gravity in four dimensions. We use N'(r) to explore definitions of curvature and of effective global dimension. An effective curvature R(v) goes from negative values for low k2 (the inverse bare Newton constant) to slightly positive values around the transition k2c. Far above the transition R(V) is hard to compute. This R(v) depends on the distance scale involved and we therefore investigate a similar explicitly r-dependent 'running' curvature R(eff)(r). This increases from values of order R(V) at intermediate distances to very high values at short distances. A global dimension d goes from high values in the region with low k2 to d = 2 at high k2. At the transition d is consistent with 4. We present evidence for scaling of N' (r) and introduce a scaling dimension d(s) which turns out to be approximately 4 in both weak and strong coupling regions. We discuss possible implications of the results, the emergence of classical euclidean spacetime and a possible 'triviality' of the theory.