Spinning up the spool: massive spinning fields in 3d quantum gravity

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

We show how to incorporate massive spinning fields into the Euclidean path integral of three-dimensional quantum gravity via its Chern–Simons formulation. The coupling of the spinning fields to gravity is captured by a Wilson spool, a collection of Wilson loops winding around closed paths of the geometry, and generalizes the proposal of Castro et al (2023 J. High Energy Phys. JHEP07(2023)120; Phys. Rev. Lett. 131 171602). We present a robust derivation of the Wilson spool by providing a new group-theoretic perspective of the quasinormal mode method for one-loop determinants. We test our proposal on Euclidean BTZ and S 3 backgrounds. We also evaluate explicitly the quantum corrections to the path integral on S 3 , and report on how G N and the mass are renormalized to leading order in perturbation theory.