Geometry and symmetries in lattice spinor gravity

TL;DR

This paper proposes a lattice spinor gravity model where geometry and symmetries emerge dynamically from fermionic degrees of freedom, unifying Euclidean and Minkowski theories and maintaining gauge and coordinate invariance.

Contribution

It introduces a novel lattice model of quantum gravity based on fermions, with emergent geometry and symmetries, unifying different spacetime signatures.

Findings

Metric and geometrical objects emerge as fermion collective fields.

The quantum effective action is invariant under general coordinate transformations.

Gauge and Lorentz symmetries are intertwined through geometrical objects.

Abstract

Lattice spinor gravity is a proposal for regularized quantum gravity based on fermionic degrees of freedom. In our lattice model the local Lorentz symmetry is generalized to complex transformation parameters. The difference between space and time is not put in a priori, and the euclidean and Minkowski quantum field theory are unified in one functional integral. The metric and its signature arise as a result of the dynamics, corresponding to a given ground state or cosmological solution. Geometrical objects as the vierbein, spin connection or the metric are expectation values of collective fields built from an even number of fermions. The quantum effective action for the metric is invariant under general coordinate transformations in the continuum limit. The action of our model is found to be also invariant under gauge transformations. We observe a "geometrical entanglement" of gauge- and Lorentz-transformations due to geometrical objects transforming non-trivially under both types of symmetry transformations.