No fermion doubling in quantum geometry

TL;DR

This paper explores how quantum geometry in loop quantum gravity may prevent the fermion doubling problem common in lattice theories, potentially enabling chiral fermions in quantum gravity frameworks.

Contribution

It proposes that superpositions of discretized states in quantum geometry could eliminate fermion doubling, allowing chiral fermions in loop quantum gravity.

Findings

Quantum geometry discretizes matter field equations.

Superpositions of states may prevent fermion doubling.

Potential for incorporating chiral fermions in loop quantum gravity.

Abstract

In loop quantum gravity the discrete nature of quantum geometry acts as a natural regulator for matter theories. Studies of quantum field theory in quantum space-times in spherical symmetry in the canonical approach have shown that the main effect of the quantum geometry is to discretize the equations of matter fields. This raises the possibility that in the case of fermion fields one could confront the usual fermion doubling problem that arises in lattice gauge theories. We suggest, again based on recent results on spherical symmetry, that since the background space-times will generically involve superpositions of states associated with different discretizations the phenomenon may not arise. This opens a possibility of incorporating chiral fermions in the framework of loop quantum gravity.