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A spool for every quotient: One-loop partition functions in AdS$_3$ gravity
by Robert Bourne, Jackson R. Fliss, Bob Knighton
Submission summary
| Authors (as registered SciPost users): | Jackson R. Fliss · Robert Knighton |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202601_00018v1 (pdf) |
| Date submitted: | Jan. 9, 2026, 9:08 a.m. |
| Submitted by: | Jackson R. Fliss |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
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.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
Please find here our resubmitted manuscript with the minor revisions requested by the two referees. The changes to the manuscript are described in our replies to the respective referee, as well as highlighted in blue in the resubmission and listed below for convenience.
On behalf of the other authors,
-Jackson Fliss
List of changes
1) Expanded paragraph under equation (2.5) clarifying why we write the connection in a split manner while working in Euclidean signature.
2) Changed $\tau$ to $\vartheta$ in sentence above equation (2.9).
3) Added a sentence to footnote 12 on the additional determinants needed to reproduce the graviton determinant from the spool expression.
4) Added paragraph in discussion section discussing the use of the Wilson spool for calculating one-loop corrections to entanglement entropy.