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Universality Class of the First Levels in Low-Dimensional Gravity

Alexander Altland ^1,*, Jeremy van der Heijden ^2,†, Tobias Micklitz ³, Moshe Rozali ^2,‡, and Joaquim Telles de Miranda ^3,§

¹Institute for Theoretical Physics, Zülpicher Straβe 77a, 50937 Cologne, Germany
²Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, British Columbia V6T 1Z1, Canada
³Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180, Rio de Janeiro, Brazil

^*Contact author: alexal@thp.uni-koeln.de
^†Contact author: jeremy.vanderheijden@ubc.ca
^‡Contact author: rozali@phas.ubc.ca
^§Contact author: joaquim@cbpf.br

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Phys. Rev. Lett. 135, 121601 – Published 15 September, 2025

DOI: https://doi.org/10.1103/5tn7-knd7

Abstract

We investigate the physics of a small group of quantum states defined above the sharply defined ground state of a chaotic ensemble. This “universality class of the first levels” is realized in the majority of “synthetic” random matrix models but, for all we know, in only one microscopically defined system: low-dimensional gravity. We discuss the physical properties of these states, notably their exceptional rigidity against external perturbations, as quantified by the so-called quantum state fidelity. Examining these structures through the lenses of random matrix and string theory, we highlight their relevance to the physics of low-dimensional holographic principles.

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Phys. Rev. Lett. 135, 121601– Published 15 September, 2025

Vol. 135, Iss. 12 — 19 September 2025

Received 3 June 2025
Accepted 12 August 2025

DOI: https://doi.org/10.1103/5tn7-knd7

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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Universality Class of the First Levels in Low-Dimensional Gravity

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