Keeping matter in the loop in dS3 quantum gravity

Abstract

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.