A spool for every quotient: One-loop partition functions in AdS$_3$ gravity, by Robert Bourne, Jackson R. Fliss, Bob Knighton
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SciPost Physics Home Authoring Refereeing Submit a manuscript About A spool for every quotient: One-loop partition functions in AdS$_3$ gravity Robert Bourne, Jackson R. Fliss, Bob Knighton SciPost Phys. 20, 065 (2026) · published 2 March 2026 doi: 10.21468/SciPostPhys.20.3.065 pdf BiBTeX RIS Submissions/Reports Abstract The Wilson spool is a prescription for expressing one-loop determinants as topological line operators in three-dimensional gravity. We extend this program to describe massive spinning fields on all smooth, cusp-free, solutions of Euclidean gravity with a negative cosmological constant. Our prescription makes use of the expression of such solutions as a quotients of hyperbolic space. The result is a gauge-invariant topological operator, which can be promoted to an off-shell operator in the gravitational path integral about a given saddle-point. When evaluated on-shell, the Wilson spool reproduces and extends the known results of one-loop determinants on hyperbolic quotients. We motivate our construction of the Wilson spool from multiple perspectives: the Selberg trace formula, worldline quantum mechanics, and the quasinormal mode method. × TY - JOURPB - SciPost FoundationDO - 10.21468/SciPostPhys.20.3.065TI - A spool for every quotient: One-loop partition functions in AdS$_3$ gravityPY - 2026/03/02UR - https://scipost.org/SciPostPhys.20.3.065JF - SciPost PhysicsJA - SciPost Phys.VL - 20IS - 3SP - 065A1 - Bourne, RobertAU - Fliss, Jackson R.AU - Knighton, BobAB - The Wilson spool is a prescription for expressing one-loop determinants as topological line operators in three-dimensional gravity. We extend this program to describe massive spinning fields on all smooth, cusp-free, solutions of Euclidean gravity with a negative cosmological constant. Our prescription makes use of the expression of such solutions as a quotients of hyperbolic space. The result is a gauge-invariant topological operator, which can be promoted to an off-shell operator in the gravitational path integral about a given saddle-point. When evaluated on-shell, the Wilson spool reproduces and extends the known results of one-loop determinants on hyperbolic quotients. We motivate our construction of the Wilson spool from multiple perspectives: the Selberg trace formula, worldline quantum mechanics, and the quasinormal mode method.ER - × @Article{10.21468/SciPostPhys.20.3.065, title={{A spool for every quotient: One-loop partition functions in AdS$_3$ gravity}}, author={Robert Bourne and Jackson R. Fliss and Bob Knighton}, journal={SciPost Phys.}, volume={20}, pages={065}, year={2026}, publisher={SciPost}, doi={10.21468/SciPostPhys.20.3.065}, url={https://scipost.org/10.21468/SciPostPhys.20.3.065},} Ontology / Topics See full Ontology or Topics database. AdS$_3$ gravity Chern-Simons theory Topological quantum field theories (TQFT) Wilson loops Authors / Affiliation: mappings to Contributors and Organizations See all Organizations. 1 Robert Bourne, 1 Jackson R. Fliss, 1 Bob Knighton 1 University of Cambridge Funders for the research work leading to this publication Science and Technology Facilities Council [STFC] Simons Foundation