Untangling Selberg from the Wilson spool: 1-loop determinants and trace formulae in (A)dS$_{3}$

Fuente: arXiv
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Autori principali: Haupfear, Samuel, Martin, Victoria, Svesko, Andrew, Zukowski, Claire
Natura: Preprint
Pubblicazione: 2025
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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