Combinatorial and topological phase structure of non-perturbative n-dimensional quantum gravity

TL;DR

This paper offers a non-perturbative, geometric analysis of n-dimensional quantum gravity, revealing a phase structure linked to manifold topology and connecting to 2D models with random triangulations.

Contribution

It introduces a new geometric framework for quantum gravity that classifies geometries by homotopy types and explores phase structures in higher dimensions.

Findings

Continuum limit exists with non-trivial phase structure.

Phase structure parametrized by homotopy types of manifolds.

Qualitative agreement with 2D quantum gravity models.

Abstract

We provide a non-perturbative geometrical characterization of the partition function of $n$-dimensional quantum gravity based on a coarse classification of riemannian geometries. We show that, under natural geometrical constraints, the theory admits a continuum limit with a non-trivial phase structure parametrized by the homotopy types of the class of manifolds considered. The results obtained qualitatively coincide, when specialized to dimension two, with those of two-dimensional quantum gravity models based on random triangulations of surfaces.