2025/07/07 by Robert Bourne, Jackson R. Fliss, Bourne, Robert +3 · 4 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #Cosmology and Gravitation Theories
paper · pdf · doi:10.21468/scipostphys.20.3.065
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.