Is de Sitter space a fermion?

TL;DR

This paper provides evidence that de Sitter space and similar geometries can be quantized as fermions within a gauge formulation of gravity, challenging traditional views on the bosonic nature of geometric spaces.

Contribution

It demonstrates, using gauge gravity, that de Sitter space can be consistently quantized as a fermion, linking geometric quantization to fermionic statistics and mathematical structures like the Skyrme model.

Findings

De Sitter space can be quantized with fermionic statistics.

The mathematics parallels the Skyrme model for baryons.

Raises fundamental questions about the bosonic or fermionic nature of geometry.

Abstract

Following up on a recent model yielding fermionic geometries, I turn to more familiar territory to address the question of statistics in purely geometric theories. Working in the gauge formulation of gravity, where geometry is characterized by a symmetry broken Cartan connection, I give strong evidence to suggest that de Sitter space itself, and a class of de Sitter-like geometries, can be consistently quantized fermionically. By this I mean that de Sitter space can be quantized such that the wavefunctional picks up an overall minus sign under a $2\pi$ rotational diffeomorphism. Surprisingly, the underlying mathematics is the same as that of the Skyrme model for strongly interacting baryons. This promotes the question {\it "Is geometry bosonic or fermionic?"} beyond the realm of the rhetorical and places it on uncomfortably familiar ground.