Discrete Gravity Models and Loop Quantum Gravity: a Short Review

TL;DR

This paper reviews the connection between Loop Quantum Gravity and discrete gravity models, comparing different geometric discretizations and their roles in spin foam formalism, highlighting the importance of simplicity constraints.

Contribution

It provides a comparative analysis of Regge and twisted geometries and discusses discrete actions and the role of simplicity constraints in spin foam models.

Findings

Comparison of Regge and twisted geometries

Discussion of discrete actions based on twisted geometries

Analysis of simplicity constraints in spin foam formalism

Abstract

We review the relation between Loop Quantum Gravity on a fixed graph and discrete models of gravity. We compare Regge and twisted geometries, and discuss discrete actions based on twisted geometries and on the discretization of the Plebanski action. We discuss the role of discrete geometries in the spin foam formalism, with particular attention to the definition of the simplicity constraints.