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  • Letter
  • Open Access

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

Felix M. Haehl

Wyatt Reeves and Moshe Rozali

  • School of Mathematical Sciences and STAG Research Centre, University of Southampton, Southampton SO17 1BJ, United Kingdom

  • Department of Physics and Astronomy, University of British Columbia, Vancouver V6T 1Z1, Canada

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Phys. Rev. D 108, L101902 – Published 6 November, 2023

DOI: https://doi.org/10.1103/PhysRevD.108.L101902

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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Phys. Rev. D 108, L101902– Published 6 November, 2023
  • Received 20 September 2023
  • Accepted 16 October 2023
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