Beyond the ensemble paradigm in low dimensional quantum gravity: Schwarzian density, quantum chaos and wormhole contributions
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866908432914710528 |
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| author | Haneder, Fabian Urbina, Juan Diego Moreno, Camilo Weber, Torsten Richter, Klaus |
| author_facet | Haneder, Fabian Urbina, Juan Diego Moreno, Camilo Weber, Torsten Richter, Klaus |
| contents | 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 ($\sinh 2π\sqrt{E}$) 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 theories and SYK models. 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_02270 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Beyond the ensemble paradigm in low dimensional quantum gravity: Schwarzian density, quantum chaos and wormhole contributions Haneder, Fabian Urbina, Juan Diego Moreno, Camilo Weber, Torsten Richter, Klaus High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics Chaotic Dynamics 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 ($\sinh 2π\sqrt{E}$) 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 theories and SYK models. 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. |
| title | Beyond the ensemble paradigm in low dimensional quantum gravity: Schwarzian density, quantum chaos and wormhole contributions |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics Chaotic Dynamics |
| url | https://arxiv.org/abs/2410.02270 |