A Regularization of Quantum Gravity

TL;DR

This paper proposes a new regularization method for two-dimensional quantum gravity using small fluctuations around equilateral triangles, supported by numerical evidence of long-range correlations, with potential for higher-dimensional generalization.

Contribution

It introduces a novel regularization approach for quantum gravity based on Regge calculus with small link fluctuations, emphasizing the necessity of a negative bare cosmological constant.

Findings

Numerical evidence of long-range correlations in the model

Regularization approach aligns with properties of an expanding universe

Potential extension of the method to higher dimensions

Abstract

We re-examine results of the Liouville theory and provide arguments that a {\it negative} bare cosmological constant is essential to define two-dimensional quantum gravity. From this we are naturally led to a regularization of quantum gravity within the Regge approach such that it is described by small fluctuations around equilateral triangles, whose average link length approaches zero in the continuum limit. We investigate a model based on this idea numerically and present evidence for the desired long-range correlations. Interestingly, the approach might generalize to higher dimensions. The picture of an inflated balloon, which is often used to demonstrate the properties of an expanding classical universe, seems to be valuable to understand quantum gravity as well.