Lattice spinor gravity

TL;DR

This paper introduces a lattice model for quantum gravity using fermions, maintaining local Lorentz symmetry and general covariance, with the metric emerging as a composite field, applicable in both Minkowski and Euclidean signatures.

Contribution

It presents a novel fermion-based lattice formulation of quantum gravity with local gauge symmetries and a dynamically generated metric, unifying Minkowski and Euclidean frameworks.

Findings

Lattice action exhibits local Lorentz symmetry.

Continuum limit is invariant under general coordinate transformations.

Metric arises as a composite field from fermions.

Abstract

We propose a regularized lattice model for quantum gravity purely formulated in terms of fermions. The lattice action exhibits local Lorentz symmetry, and the continuum limit is invariant under general coordinate transformations. The metric arises as a composite field. Our lattice model involves no signature for space and time, describing simultaneously a Minkowski or euclidean theory. It is invariant both under Lorentz transformations and euclidean rotations. The difference between space and time arises from expectation values of composite fields. Our formulation includes local gauge symmetries beyond the generalized Lorentz symmetry. The lattice construction can be employed for formulating models with local gauge symmetries purely in terms of fermions