Untangling Selberg from the Wilson spool: 1-loop determinants and trace formulae in (A)dS$_{3}$
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915652524048384 |
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| author | Haupfear, Samuel Martin, Victoria Svesko, Andrew Zukowski, Claire |
| author_facet | Haupfear, Samuel Martin, Victoria Svesko, Andrew Zukowski, Claire |
| contents | Leading quantum effects in perturbative quantum gravity are captured by functional determinants of kinetic operators. We study such 1-loop determinants in three-dimensional Euclidean (anti-) de Sitter gravity evaluated using two seemingly disparate tools, the Selberg zeta function and the Wilson spool. For the Euclidean BTZ black hole, we demonstrate the Wilson spool for massive bosons of arbitrary spin directly equates to a representation-theoretic version of the Selberg zeta function. In the case of Euclidean de Sitter, we show a new trace formula associated with the Fredholm determinant for the scalar Laplacian on the three-sphere reproduces the Wilson spool. Generalizing the trace formula, we comment on how to extend this Wilson spool construction to lens space quotients and higher-dimensional spheres. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_05358 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Untangling Selberg from the Wilson spool: 1-loop determinants and trace formulae in (A)dS$_{3}$ Haupfear, Samuel Martin, Victoria Svesko, Andrew Zukowski, Claire High Energy Physics - Theory General Relativity and Quantum Cosmology Leading quantum effects in perturbative quantum gravity are captured by functional determinants of kinetic operators. We study such 1-loop determinants in three-dimensional Euclidean (anti-) de Sitter gravity evaluated using two seemingly disparate tools, the Selberg zeta function and the Wilson spool. For the Euclidean BTZ black hole, we demonstrate the Wilson spool for massive bosons of arbitrary spin directly equates to a representation-theoretic version of the Selberg zeta function. In the case of Euclidean de Sitter, we show a new trace formula associated with the Fredholm determinant for the scalar Laplacian on the three-sphere reproduces the Wilson spool. Generalizing the trace formula, we comment on how to extend this Wilson spool construction to lens space quotients and higher-dimensional spheres. |
| title | Untangling Selberg from the Wilson spool: 1-loop determinants and trace formulae in (A)dS$_{3}$ |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2507.05358 |