Fermions on Quantum Geometry and Resolution of Doubling Problem

TL;DR

This paper demonstrates that in Loop Quantum Gravity, superpositions of quantum geometries can suppress fermion doubling, potentially resolving a key issue in reconciling fermions with discrete spacetime.

Contribution

The work introduces a novel approach using superposed quantum geometries in Loop Quantum Gravity to address the fermion doubling problem.

Findings

Fermion doubler modes are suppressed in the quantum geometry propagator.

Superposition of lattice-refined states resolves fermion doubling.

Results suggest a natural continuum limit in quantum gravity.

Abstract

The fermion doubling problem has an important impact on quantum gravity, by revealing the tension between fermion and the fundamental discreteness of quantum spacetime. In this work, we discover that in Loop Quantum Gravity, the quantum geometry involving superposition of states associated with lattice refinements provides a resolution to the fermion doubling problem. We construct and analyze the fermion propagator on the quantum geometry, and we show that all fermion doubler modes are suppressed in the propagator. Our result suggests that the superposition nature of quantum geometry should resolve the tension between fermion and the fundamental discreteness, and relate to the continuum limit of quantum gravity.