We propose a mechanism that couples matter fields to three-dimensional quantum gravity, which can be used for theories with a positive or negative cosmological constant. Our proposal is rooted in the Chern-Simons formulation of three-dimensional gravity and makes use of the Wilson spool, a collection of Wilson loops winding around closed paths of the background. We show that the Wilson spool correctly reproduces the one-loop determinant of a free massive scalar field on rotating black holes in ${\mathrm{AdS}}_3$ and Euclidean ${\mathrm{dS}}_3$ as $G_N\to 0$. Moreover, we describe how to incorporate quantum metric fluctuations into this formalism.

• Received 22 April 2023
• Revised 14 July 2023
• Accepted 22 September 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.171602

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society