Discrete structures in gravity

TL;DR

This paper reviews discrete approaches to classical and quantum gravity, focusing on piecewise-linear models, their generalizations to four dimensions, and their connections to topological theories, highlighting recent progress and implications.

Contribution

It provides a comprehensive overview of discrete gravity models, especially 3D and 4D quantum models involving 6j-symbols, and discusses their extensions and theoretical implications.

Findings

Progress in generalizing 3D quantum gravity models to 4D.

Connections established between discrete gravity models and topological theories.

Implications for the original edge-length variable formulation of discrete gravity.

Abstract

Discrete approaches to gravity, both classical and quantum, are reviewed briefly, with emphasis on the method using piecewise-linear spaces. Models of 3-dimensional quantum gravity involving 6j-symbols are then described, and progress in generalising these models to four dimensions is discussed, as is the relationship of these models in both three and four dimensions to topological theories. Finally, the repercussions of the generalisations are explored for the original formulation of discrete gravity using edge-length variables.