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Beyond the ensemble paradigm in low-dimensional quantum gravity: Schwarzian density, quantum chaos, and wormhole contributions

Fabian Haneder*, Juan Diego Urbina, Camilo Moreno, Torsten Weber, and Klaus Richter

  • *Contact author: fabian.haneder@ur.de
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Phys. Rev. D 111, 126015 – Published 20 June, 2025

DOI: https://doi.org/10.1103/rsrq-l6z8

Abstract

Based on periodic orbit theory, we address the individual-system versus ensemble interpretation of quantum gravity from a quantum chaos perspective. To this end, we show that the spectrum of geodesic motion on high-dimensional hyperbolic manifolds, described by the Selberg trace formula, displays a Schwarzian (sinh2πE) mean level density. Due to its chaotic classical limit, this quantum system also shows all universal signatures of quantum chaos. These two properties imply a possible duality to Jackiw-Teitelboim-type quantum gravity at the level of a single system instead of an ensemble of systems like matrix- and Sachdev-Ye-Kitaev models. Moving beyond the universal regime, we show how the full wormhole geometry on the gravity side emerges from the discreteness of the set of periodic orbits. Thereby, we take initial steps towards a duality between gravitational and mesoscopic chaotic quantum systems through the topological, respectively, periodic orbit expansions of their correlators.

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Phys. Rev. D 111, 126015– Published 20 June, 2025
  • Received 31 October 2024
  • Accepted 1 June 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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