New action for simplicial gravity in four dimensions

TL;DR

This paper proposes a new simplicial gravity model in four dimensions using spinors as fundamental variables, connecting it to loop quantum gravity and twisted geometries, and discussing its quantum implications.

Contribution

It introduces a novel action for four-dimensional simplicial gravity with spinors, incorporating Hamiltonian and gauge symmetries, and explores its relation to existing quantum gravity frameworks.

Findings

The model has a well-defined Hamiltonian structure.

It relates to loop quantum gravity and twisted geometries.

Comments on the quantum theory implications are provided.

Abstract

We develop a proposal for a theory of simplicial gravity with spinors as the fundamental configuration variables. The underlying action describes a mechanical system with finitely many degrees of freedom, the system has a Hamiltonian and local gauge symmetries. We will close with some comments on the resulting quantum theory, and explain the relation to loop quantum gravity and twisted geometries. The paper appears in parallel with an article by Cort\^es and Smolin, who study the relevance of the model for energetic causal sets and various other approaches to quantum gravity.