On the exponential bound in four dimensional simplicial gravity

TL;DR

This paper investigates the exponential bound in four-dimensional simplicial quantum gravity, focusing on the growth rate of triangulations of the 4-sphere to ensure the model's mathematical consistency.

Contribution

It analyzes the exponential bound condition in 4D simplicial gravity and discusses numerical evidence supporting such bounds.

Findings

Numerical simulations support exponential bounds on triangulation counts.

The model's well-definedness depends on these exponential bounds.

Supports the use of simplicial quantum gravity as a regularization for 4D quantum gravity.

Abstract

Simplicial quantum gravity has been proposed as a regularization for four dimensional quantum gravity. The partition function is constructed by performing a weighted sum over all triangulations of the 4-sphere. The model is well-defined only if the number of such triangulations consisting of $N$ simplexes is exponentially bounded. Numerical simulations seem so far to favor such a bound.