Is geometry bosonic or fermionic?

TL;DR

This paper explores whether geometric structures in a torsional gravity theory can exhibit fermionic behavior upon quantization, challenging the assumption that gravity is solely bosonic by mapping the model onto the Skyrme model.

Contribution

It introduces a torsional gravity model that can produce fermionic geometric structures, providing a novel link between geometry and fermionic quantization.

Findings

Localized geometric structures can be quantized as fermions

The model can be mapped onto the Skyrme model of baryons

Questions the traditional view of gravity as purely bosonic

Abstract

It is generally assumed that the gravitational field is bosonic. Here we show that a simple propagating torsional theory can give rise to localized geometric structures that can consistently be quantized as fermions under exchange. To demonstrate this, we show that the model can be formally mapped onto the Skyrme model of baryons, and we use well-known results from Skyrme theory. This begs the question: {\it Is geometry bosonic or fermionic (or both)?}