An entropic puzzle in periodic dilaton gravity and DSSYK
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Author(s)
Blommaert, Andreas
Levine, Adam
Mertens, Thomas G.
Papalini, Jacopo
Parmentier, Klaas
Date Issued
July 7, 2025
Journal
Journal of High Energy Physics
Publisher
Springer Berlin Heidelberg
Citation
Blommaert, A., Levine, A., Mertens, T.G. et al. An entropic puzzle in periodic dilaton gravity and DSSYK. J. High Energ. Phys. 2025, 93 (2025).
Version
Final published version
Abstract
We study 2d dilaton gravity theories with a periodic potential, with special emphasis on sine dilaton gravity, which is holographically dual to double-scaled SYK. The periodicity of the potentials implies a symmetry under (discrete) shifts in the momentum conjugate to the length of geodesic slices. This results in divergences. The correct definition is to gauge this symmetry. This discretizes the geodesic lengths. Lengths below a certain threshold are null states. Because of these null states, the entropy deviates drastically from Bekenstein-Hawking and the Hilbert space becomes finite dimensional. The spacetimes have a periodic radial coordinate. These are toy models of 2d quantum cosmology with a normalizable wavefunction. We study two limiting dualities: one between flat space quantum gravity and the Heisenberg algebra, and one between topological gravity and the Gaussian matrix integral. We propose an exact density of states for certain classes of periodic dilaton gravity models.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
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DOI of Published Version
https://doi.org/10.1007/JHEP07(2025)093
