More on the Exponential Bound of Four Dimensional Simplicial Quantum Gravity

A crucial requirement for the standard interpretation of Monte Carlo simulations of simplicial quantum gravity is the existence of an exponential bound that makes the partition function well-defined. We present numerical data favoring the existence of an exponential bound, and we argue that the more limited data sets on which recently opposing claims were based are also consistent with the existence of an exponential bound. 1 Introduction Theories that we hope could be connected to Euclidean quantum gravity can be investigated through Monte Carlo simulations of discrete models, one of the most popular approaches being dynamical triangulations of simplicial quantum gravity. Here we consider the four dimensional theory without matter but with a cosmological constant for fixed topology M = S 4 [1, 2, 3, 4]. The most attractive feature of this model is that there is evidence for a second order phase transition and therefore a continuum limit may exist. In this language the Einstein-Hi..