Euclidean wormholes in two-dimensional conformal field theories from quantum chaos and number theory

Haehl, Felix M., Reeves, Wyatt and Rozali, Moshe (2023) Euclidean wormholes in two-dimensional conformal field theories from quantum chaos and number theory. Phys.Rev.D, 108 (10), [L101902]. (doi:10.1103/PhysRevD.108.L101902).

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Abstract

We consider two-dimensional conformal field theories (CFTs) that exhibit a hallmark feature of quantum chaos: universal repulsion of energy levels as described by a regime of linear growth of the spectral form factor. This physical input together with modular invariance strongly constrains the spectral correlations and the subleading corrections to the linear growth. We show that these are determined by the Kuznetsov trace formula, which highlights an intricate interplay of universal physical properties of chaotic CFTs and analytic number theory. The trace formula manifests the fact that the simplest possible CFT correlations consistent with quantum chaos are precisely those described by a Euclidean wormhole in AdS₃ gravity with [torus]×[interval] topology. For contrast, we also discuss examples of nonchaotic CFTs in this language.

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Accepted/In Press date: 16 October 2023

e-pub ahead of print date: 6 November 2023

Published date: 15 November 2023

Additional Information: Funding Information: The authors thank S. Collier and E. Perlmutter for helpful conversations and comments. F. M. H. is supported by the UKRI Frontier Research Guarantee [EP/X030334/1]. M. R. and W. R. are supported by a Discovery Grant from NSERC. Publisher Copyright: © 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"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.