Keeping matter in the loop in dS₃ quantum gravity

This is the authors' abstract. We don't add key points for this paper.

We propose a mechanism that couples matter fields to three-dimensional de Sitter quantum gravity. Our construction is based on the Chern-Simons formulation of three-dimensional Euclidean gravity, and it centers on a collection of Wilson loops winding around Euclidean de Sitter space. We coin this object a Wilson spool. To construct the spool, we build novel representations of su(2). To evaluate the spool, we adapt and exploit several known exact results in Chern-Simons theory. Our proposal correctly reproduces the one-loop determinant of a free massive scalar field on S³ as GN→ 0. Moreover, allowing for quantum metric fluctuations, it can be systematically evaluated to any order in perturbation theory.