Towards lattice-regularized Quantum Gravity

TL;DR

This paper develops a lattice-regularized quantum gravity model based on the Cartan formulation, incorporating fermions and local Lorentz invariance, aiming to unify gravity with the Standard Model.

Contribution

It introduces a well-defined lattice quantum gravity theory using fermion-based tetrads, maintaining local Lorentz invariance and potential for unification with the Standard Model.

Findings

Constructs a non-perturbative lattice quantum gravity model.

Ensures invariance under local Lorentz and diffeomorphism transformations.

Provides a framework that could reproduce General Relativity in the continuum limit.

Abstract

Using the Cartan formulation of General Relativity, we construct a well defined lattice-regularized theory capable to describe large non-perturbative quantum fluctuations of the frame field (or the metric) and of the spin connection. To that end we need to present the tetrad by a composite field built as a bilinear combination of fermion fields. The theory is explicitly invariant under local Lorentz transformations and, in the continuum limit, under general covariant transformations, or diffeomorphisms. Being well defined for large and fast varying fields at the ultraviolet cutoff, the theory simultaneously has chances of reproducing standard General Relativity in the infrared continuum limit. The present regularization of quantum gravity opens new possibilities of its unification with the Standard Model.