Göttingen 2025 – wissenschaftliches Programm

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 2: Mathematical Materials Science and AdS/CFT

MP 2.5: Vortrag

Dienstag, 1. April 2025, 15:25–15:45, ZHG001

Towards identifying a genus expansion in the Selberg trace formula — •Fabian Haneder, Juan Diego Urbina, Torsten Weber, and Klaus Richter — Universität Regensburg, Regensburg, Deutschland

Jackiw-Teitelboim (JT) gravity has been a useful tool for advancing our understanding of several features believed to be generic in quantum gravity, such as the density of states (exponentially growing for black hole systems), wormholes and topological expansions of the gravitational path integral.

Key progress in doing so has been made using random matrix universality, both for orientable [Saad et al., arXiv:2210.11565, Weber et al., Weber et al., 2023 J. Phys. A: Math. Theor. 56 205206] and unorientable [Weber et al., J. High Energ. Phys. 2024, 267 (2024), Tall et al., arXiv:2411.08129] JT gravity, establishing the quantum chaoticity of the theory. In an effort to go beyond the universal regime, we use periodic orbit theory, which has been used precisely to derive universality, and study non-universal features, for quantum chaotic systems.

After reviewing recent success [Haneder et al., arXiv:2410.02270] in capturing the exact (leading genus) density of states and wormhole amplitude of JT gravity with a single quantum chaotic system, we report on our progress in identifying a topological expansion, reminiscent of the one in JT gravity, in the same system, a particle moving on a high-dimensional hyperbolic manifold. To describe the system, we make use of the Selberg trace formula, which renders periodic orbit theory exact.

Keywords: JT gravity; Quantum Chaos; Holography; Selberg Trace Formula