Fermions in loop quantum gravity: a new approach to the doubling problem

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 the quantum geometry involving the superposition of states associated with lattice refinements in Loop Quantum Gravity provides a resolution to the fermion doubling problem. We construct and analyze the fermion propagator on the quantum geometry, showing 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.