A left-handed simplicial action for euclidean general relativity

TL;DR

This paper introduces a novel simplicial action for Euclidean general relativity using only left-handed fields, which converges to the continuum theory and simplifies the field equations compared to existing models.

Contribution

It presents a new left-handed simplicial action that converges to continuum GR and is simpler than the Regge model, including an analogous hypercubic lattice formulation.

Findings

The proposed action converges to continuum GR in the limit.

The new model's equations are simpler than the Regge model.

An analogous hypercubic lattice theory is also developed.

Abstract

An action for simplicial euclidean general relativity involving only left-handed fields is presented. The simplicial theory is shown to converge to continuum general relativity in the Plebanski formulation as the simplicial complex is refined. This contrasts with the Regge model for which Miller and Brewin have shown that the full field equations are much more restrictive than Einstein's in the continuum limit. The action and field equations of the proposed model are also significantly simpler then those of the Regge model when written directly in terms of their fundamental variables. An entirely analogous hypercubic lattice theory, which approximates Plebanski's form of general relativity is also presented.